Year 4: Acute and obtuse angles
Part of the Year 4 shapes, angles and symmetry chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Acute and obtuse angles
We use a right angle to describe other angles. The corner of a piece of paper is a right angle, so you can use it as an angle tester: put it on one arm of an angle and see where the other arm goes.
- An angle smaller than a right angle is acute. It is sharp, like the tip of a pencil.
- An angle bigger than a right angle but smaller than a straight line is obtuse. It is wide open.
- An angle of two right angles is a straight line.
Comparing angles. To compare two angles, look at how far apart the two arms are. The wider the opening, the bigger the angle. The length of the arms does not matter. You can draw an angle with very long arms, and it can still be small.
Ordering angles. To put angles in order, first sort them: acute angles are the smallest, then a right angle, then obtuse angles. Then compare angles in the same group by how wide they open.
Angles in shapes. Every corner of a shape is an angle. You can use the angle tester on each corner. A triangle can have acute angles, a right angle or one obtuse angle.
Key ideas
- Acute: smaller than a right angle. Right angle: a quarter turn. Obtuse: bigger than a right angle, smaller than a straight line.
- A straight line is an angle of two right angles.
- Use the corner of a piece of paper as an angle tester.
- Compare angles by how wide they open, not by how long the arms are.
- To order angles: acute first, then right angle, then obtuse. Then compare inside each group.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Compare the angle with a right angle (the corner of a piece of paper). Smaller is acute. The same is a right angle. Bigger, but less than a straight line, is obtuse.
- Put the paper corner on one arm of the angle. The dashed lines show the corner of the paper.
- Look at the other arm. Is it inside the corner, on the corner, or past the corner?The other arm is inside the paper corner. The angle is smaller than a right angle.
- Name the angle. It is acute.
Check. Acute < right angle < obtuse < straight line. ✓
Watch out. Look at how wide the angle opens, not how long the arms are.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Compare the angle with a right angle (the corner of a piece of paper). Smaller is acute. The same is a right angle. Bigger, but less than a straight line, is obtuse.
- Put the paper corner on one arm of the angle. The dashed lines show the corner of the paper.
- Look at the other arm. Is it inside the corner, on the corner, or past the corner?The other arm is outside the paper corner. It is bigger than a right angle, but it is smaller than a straight line.
- Name the angle. It is obtuse.
Check. Acute < right angle < obtuse < straight line. ✓
Watch out. Look at how wide the angle opens, not how long the arms are.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Compare the angle with a right angle (the corner of a piece of paper). Smaller is acute. The same is a right angle. Bigger, but less than a straight line, is obtuse.
- Put the paper corner on one arm of the angle. The dashed lines show the corner of the paper.
- Look at the other arm. Is it inside the corner, on the corner, or past the corner?The two arms make one straight line. That is two right angles.
- Name the angle. It is a straight line (two right angles).
Check. Acute < right angle < obtuse < straight line. ✓
Watch out. Look at how wide the angle opens, not how long the arms are.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Compare how wide each angle opens. Use the corner of a piece of paper to help. The biggest angle opens the widest.
- Test each angle with the paper corner. The dashed lines show a right angle on each one.AB
- Sort them. Acute is smaller than a right angle. Obtuse is bigger.A: acute
B: acute - Find the biggest angle. Look at the group that has the biggest angles, then compare the openings.The biggest angle is B.
Check. No other angle opens wider than B. ✓
Watch out. Do not choose the angle with the longest arms. Look at the opening.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Sort the angles into acute, right and obtuse using the corner of a piece of paper. Acute angles are the smallest. Then compare the angles that are in the same group.
- Test each angle with the paper corner. The dashed lines show the paper corner on each angle.ABCD
- Sort them into groups. Acute angles are smaller than a right angle. Obtuse angles are bigger than a right angle.B and D: acute (smaller than a right angle)
A and C: obtuse (bigger than a right angle) - Compare the angles in the same group. The wider the opening, the bigger the angle. Ignore how long the arms are.B < D < C < A
- Write the order. Start with the smallest.B, D, C, A
Check. Look at the first and last angle: B is the smallest and A is the biggest. ✓
Watch out. A long arm does not make an angle bigger. Only the size of the opening matters.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Compare each angle of the shape with a right angle. The obtuse angle is the one that is bigger than a right angle.
- Look at each angle. The orange marks show the angles. A small square means a right angle.
- Test each angle with the paper corner. Smaller than the paper corner is acute. Bigger is obtuse.Angle A: obtuse
Angle B: acute
Angle C: acute - Choose the angle. The obtuse angle is at A.
Check. Angle A really is obtuse. ✓
Watch out. Check every corner.
Watch out
Long arms do not make a bigger angle. Angle size is the amount of turn between the arms. Two angles can have arms of different lengths and still be the same size. Also take care with the words: acute is the small angle and obtuse is the wide one.Exercise 9B Acute, right and obtuse angles
Non-calculatorKey words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Compare the angle with a right angle (the corner of a piece of paper). Smaller is acute. The same is a right angle. Bigger, but less than a straight line, is obtuse.
- Put the paper corner on one arm of the angle. The dashed lines show the corner of the paper.
- Look at the other arm. Is it inside the corner, on the corner, or past the corner?The other arm is inside the paper corner. The angle is smaller than a right angle.
- Name the angle. It is acute.
Check. Acute < right angle < obtuse < straight line. ✓
Watch out. Look at how wide the angle opens, not how long the arms are.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Compare the angle with a right angle (the corner of a piece of paper). Smaller is acute. The same is a right angle. Bigger, but less than a straight line, is obtuse.
- Put the paper corner on one arm of the angle. The dashed lines show the corner of the paper.
- Look at the other arm. Is it inside the corner, on the corner, or past the corner?The other arm lines up exactly with the paper corner.
- Name the angle. It is a right angle.
Check. Acute < right angle < obtuse < straight line. ✓
Watch out. Look at how wide the angle opens, not how long the arms are.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Compare the angle with a right angle (the corner of a piece of paper). Smaller is acute. The same is a right angle. Bigger, but less than a straight line, is obtuse.
- Put the paper corner on one arm of the angle. The dashed lines show the corner of the paper.
- Look at the other arm. Is it inside the corner, on the corner, or past the corner?The other arm is outside the paper corner. It is bigger than a right angle, but it is smaller than a straight line.
- Name the angle. It is obtuse.
Check. Acute < right angle < obtuse < straight line. ✓
Watch out. Look at how wide the angle opens, not how long the arms are.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Compare the angle with a right angle (the corner of a piece of paper). Smaller is acute. The same is a right angle. Bigger, but less than a straight line, is obtuse.
- Put the paper corner on one arm of the angle. The dashed lines show the corner of the paper.
- Look at the other arm. Is it inside the corner, on the corner, or past the corner?The other arm is inside the paper corner. The angle is smaller than a right angle.
- Name the angle. It is acute.
Check. Acute < right angle < obtuse < straight line. ✓
Watch out. Look at how wide the angle opens, not how long the arms are.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Compare the angle with a right angle (the corner of a piece of paper). Smaller is acute. The same is a right angle. Bigger, but less than a straight line, is obtuse.
- Put the paper corner on one arm of the angle. The dashed lines show the corner of the paper.
- Look at the other arm. Is it inside the corner, on the corner, or past the corner?The other arm is inside the paper corner. The angle is smaller than a right angle.
- Name the angle. It is acute.
Check. Acute < right angle < obtuse < straight line. ✓
Watch out. Look at how wide the angle opens, not how long the arms are.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Compare the angle with a right angle (the corner of a piece of paper). Smaller is acute. The same is a right angle. Bigger, but less than a straight line, is obtuse.
- Put the paper corner on one arm of the angle. The dashed lines show the corner of the paper.
- Look at the other arm. Is it inside the corner, on the corner, or past the corner?The other arm is outside the paper corner. It is bigger than a right angle, but it is smaller than a straight line.
- Name the angle. It is obtuse.
Check. Acute < right angle < obtuse < straight line. ✓
Watch out. Look at how wide the angle opens, not how long the arms are.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Compare the angle with a right angle (the corner of a piece of paper). Smaller is acute. The same is a right angle. Bigger, but less than a straight line, is obtuse.
- Put the paper corner on one arm of the angle. The dashed lines show the corner of the paper.
- Look at the other arm. Is it inside the corner, on the corner, or past the corner?The other arm is outside the paper corner. It is bigger than a right angle, but it is smaller than a straight line.
- Name the angle. It is obtuse.
Check. Acute < right angle < obtuse < straight line. ✓
Watch out. Look at how wide the angle opens, not how long the arms are.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Compare the angle with a right angle (the corner of a piece of paper). Smaller is acute. The same is a right angle. Bigger, but less than a straight line, is obtuse.
- Put the paper corner on one arm of the angle. The dashed lines show the corner of the paper.
- Look at the other arm. Is it inside the corner, on the corner, or past the corner?The other arm is inside the paper corner. The angle is smaller than a right angle.
- Name the angle. It is acute.
Check. Acute < right angle < obtuse < straight line. ✓
Watch out. Look at how wide the angle opens, not how long the arms are.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Use what you know: acute angles are smaller than a right angle
- Think about the meaning. acute angles are smaller than a right angleThe missing word is acute.
- Write the answer. Check it makes sense in the sentence.acute
Check. Read the sentence again with the word acute. ✓
Watch out. Acute is the small angle; obtuse is the wide one.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Use what you know: obtuse angles are bigger than a right angle but smaller than a straight line
- Think about the meaning. obtuse angles are bigger than a right angle but smaller than a straight lineThe missing word is obtuse.
- Write the answer. Check it makes sense in the sentence.obtuse
Check. Read the sentence again with the word obtuse. ✓
Watch out. Acute is the small angle; obtuse is the wide one.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Use what you know: two quarter turns make a half turn, which is a straight line
- Think about the meaning. two quarter turns make a half turn, which is a straight lineThe missing word is straight line.
- Write the answer. Check it makes sense in the sentence.straight line
Check. Read the sentence again with the word straight line. ✓
Watch out. Acute is the small angle; obtuse is the wide one.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Use what you know: a quarter turn is one right angle
- Think about the meaning. a quarter turn is one right angleThe missing word is right angle.
- Write the answer. Check it makes sense in the sentence.right angle
Check. Read the sentence again with the word right angle. ✓
Watch out. Acute is the small angle; obtuse is the wide one.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Compare how wide each angle opens. Use the corner of a piece of paper to help. The biggest angle opens the widest.
- Test each angle with the paper corner. The dashed lines show a right angle on each one.ABCD
- Sort them. Acute is smaller than a right angle. Obtuse is bigger.A: acute
B: obtuse
C: acute
D: obtuse - Find the biggest angle. Look at the group that has the biggest angles, then compare the openings.The biggest angle is B.
Check. No other angle opens wider than B. ✓
Watch out. Do not choose the angle with the longest arms. Look at the opening.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Compare how wide each angle opens. Use the corner of a piece of paper to help. The smallest angle opens the least.
- Test each angle with the paper corner. The dashed lines show a right angle on each one.ABCD
- Sort them. Acute is smaller than a right angle. Obtuse is bigger.A: obtuse
B: acute
C: obtuse
D: acute - Find the smallest angle. Look at the group that has the smallest angles, then compare the openings.The smallest angle is B.
Check. No other angle opens less than B. ✓
Watch out. Do not choose the angle with the longest arms. Look at the opening.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Sort the angles into acute, right and obtuse using the corner of a piece of paper. Acute angles are the smallest. Then compare the angles that are in the same group.
- Test each angle with the paper corner. The dashed lines show the paper corner on each angle.ABCD
- Sort them into groups. Acute angles are smaller than a right angle. Obtuse angles are bigger than a right angle.B and D: acute (smaller than a right angle)
A and C: obtuse (bigger than a right angle) - Compare the angles in the same group. The wider the opening, the bigger the angle. Ignore how long the arms are.B < D < A < C
- Write the order. Start with the smallest.B, D, A, C
Check. Look at the first and last angle: B is the smallest and C is the biggest. ✓
Watch out. A long arm does not make an angle bigger. Only the size of the opening matters.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. At an o’clock time the minute hand points at 12. Find the angle between the two hands. Each hour on a clock is one twelfth of a whole turn.
- Look at the clock. The orange mark shows the angle between the minute hand and the hour hand.
- Count the hours between the hands. Use the shorter way round. A right angle is 3 hours (12 to 3). A straight line is 6 hours (12 to 6).The hands are 2 hours apart.
- Name the angle. Less than 3 hours is acute. 3 hours is a right angle. More than 3 and less than 6 is obtuse. 6 hours is a straight line.It is acute.
Check. 3 o’clock is a right angle, so 2 o’clock is smaller. ✓
Watch out. Use the shorter way round between the hands.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. At an o’clock time the minute hand points at 12. Find the angle between the two hands. Each hour on a clock is one twelfth of a whole turn.
- Look at the clock. The orange mark shows the angle between the minute hand and the hour hand.
- Count the hours between the hands. Use the shorter way round. A right angle is 3 hours (12 to 3). A straight line is 6 hours (12 to 6).The hands are 3 hours apart.
- Name the angle. Less than 3 hours is acute. 3 hours is a right angle. More than 3 and less than 6 is obtuse. 6 hours is a straight line.It is a right angle.
Check. 3 o’clock: the hour hand and minute hand make a quarter turn at 3 and 9 o’clock. ✓
Watch out. Use the shorter way round between the hands.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. At an o’clock time the minute hand points at 12. Find the angle between the two hands. Each hour on a clock is one twelfth of a whole turn.
- Look at the clock. The orange mark shows the angle between the minute hand and the hour hand.
- Count the hours between the hands. Use the shorter way round. A right angle is 3 hours (12 to 3). A straight line is 6 hours (12 to 6).The hands are 5 hours apart.
- Name the angle. Less than 3 hours is acute. 3 hours is a right angle. More than 3 and less than 6 is obtuse. 6 hours is a straight line.It is obtuse.
Check. 3 o’clock is a right angle, so 5 o’clock is bigger. ✓
Watch out. Use the shorter way round between the hands.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. At an o’clock time the minute hand points at 12. Find the angle between the two hands. Each hour on a clock is one twelfth of a whole turn.
- Look at the clock. The orange mark shows the angle between the minute hand and the hour hand.
- Count the hours between the hands. Use the shorter way round. A right angle is 3 hours (12 to 3). A straight line is 6 hours (12 to 6).The hands are 6 hours apart.
- Name the angle. Less than 3 hours is acute. 3 hours is a right angle. More than 3 and less than 6 is obtuse. 6 hours is a straight line.It is a straight line.
Check. 3 o’clock is a right angle, so 6 o’clock is bigger. ✓
Watch out. Use the shorter way round between the hands.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Compare each angle of the shape with a right angle. The obtuse angle is the one that is bigger than a right angle.
- Look at each angle. The orange marks show the angles. A small square means a right angle.
- Test each angle with the paper corner. Smaller than the paper corner is acute. Bigger is obtuse.Angle A: obtuse
Angle B: acute
Angle C: acute - Choose the angle. The obtuse angle is at A.
Check. Angle A really is obtuse. ✓
Watch out. Check every corner.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Look at each angle (corner) of the parallelogram and sort it as acute, right or obtuse. Then count the acute ones.
- Look at the angles in the shape. The orange marks show every angle.
- Sort the angles. Acute is smaller than a right angle. Obtuse is bigger than a right angle.Angle A: acute
Angle B: obtuse
Angle C: acute
Angle D: obtuse - Count the acute angles. There are 2 acute angles.
Check. 2 acute + 0 right + 2 obtuse = 4 angles in total. ✓
Watch out. Count every corner of the shape, once each.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Look at each angle (corner) of the parallelogram and sort it as acute, right or obtuse. Then count the obtuse ones.
- Look at the angles in the shape. The orange marks show every angle.
- Sort the angles. Acute is smaller than a right angle. Obtuse is bigger than a right angle.Angle A: acute
Angle B: obtuse
Angle C: acute
Angle D: obtuse - Count the obtuse angles. There are 2 obtuse angles.
Check. 2 acute + 0 right + 2 obtuse = 4 angles in total. ✓
Watch out. Count every corner of the shape, once each.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Look at each angle (corner) of the regular hexagon and sort it as acute, right or obtuse. Then count the obtuse ones.
- Look at the angles in the shape. The orange marks show every angle.
- Sort the angles. Acute is smaller than a right angle. Obtuse is bigger than a right angle.Angle A: obtuse
Angle B: obtuse
Angle C: obtuse
Angle D: obtuse
Angle E: obtuse
Angle F: obtuse - Count the obtuse angles. There are 6 obtuse angles.
Check. 0 acute + 0 right + 6 obtuse = 6 angles in total. ✓
Watch out. Count every corner of the shape, once each.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Look at each angle (corner) of the regular octagon and sort it as acute, right or obtuse. Then count the obtuse ones.
- Look at the angles in the shape. The orange marks show every angle.
- Sort the angles. Acute is smaller than a right angle. Obtuse is bigger than a right angle.Angle A: obtuse
Angle B: obtuse
Angle C: obtuse
Angle D: obtuse
Angle E: obtuse
Angle F: obtuse
Angle G: obtuse
Angle H: obtuse - Count the obtuse angles. There are 8 obtuse angles.
Check. 0 acute + 0 right + 8 obtuse = 8 angles in total. ✓
Watch out. Count every corner of the shape, once each.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Add up the acute and right angles. Take that total away from the number of angles Mei draws. What is left must be obtuse.
- Add the acute and right angles. These are the angles that are not obtuse.4 + 2 = 6
- Take the total away from 9. Mei drew 9 angles altogether.9 − 6 = 3
- Write the answer. All the other angles are obtuse.Mei draws 3 obtuse angles.
Check. 4 acute + 2 right + 3 obtuse = 9 angles. ✓
Watch out. There are only three kinds here, so what is left over is obtuse.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Compare how wide the two angles open. The length of the arms is not important.
- Look at Leo’s idea. Leo says angle A is bigger because its arms are longer.Leo: “A has longer arms, so A is bigger.”
- Test both angles with the paper corner. The dashed lines show a right angle on each one.AB
- Compare the openings. Angle A is smaller than a right angle, so it is acute. Angle B is bigger than a right angle, so it is obtuse.A is acute. B is obtuse. B is bigger.
- Answer. No, Leo is wrong. Angle B is bigger even though its arms are shorter.
Check. An obtuse angle (B) is always bigger than an acute angle (A). ✓
Watch out. Arm length does not change the size of an angle.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. An obtuse angle is bigger than a right angle by definition.
- Remember the meaning. Obtuse means bigger than a right angle but smaller than a straight line.obtuse > 1 right angle
- Test some angles. Try 100° (just over a right angle) and 170° (nearly a straight line).Both are bigger than a right angle.
- Decide. This is always true.
Check. The word obtuse always means more than a right angle. ✓
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Try some pairs of acute angles. Add them and look at the total.
- Try a small pair. Two small acute angles.30° + 40° = 70°, which is acute.
- Try a bigger pair. Two bigger acute angles.60° + 70° = 130°, which is obtuse.
- Decide. It depends on the angles.This is sometimes true.
Check. We found one pair that gives acute and one that gives obtuse. ✓
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. A right angle is exactly a quarter turn. Acute angles are smaller than that.
- Remember the meaning of acute. Acute is smaller than a right angle.acute < right angle
- Compare. A right angle is not smaller than itself.A right angle is not acute.
- Decide. This is never true.
Check. A right angle is a different kind of angle. ✓
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. An obtuse angle is bigger than one right angle. Two of them are bigger than two right angles. See how that compares with a straight line.
- Remember what obtuse means. It is bigger than 1 right angle.each obtuse angle > 1 right angle
- Put two obtuse angles together. Two things that are each bigger than 1 right angle make more than 2 right angles.two obtuse angles > 2 right angles
- Compare with a straight line. A straight line is exactly 2 right angles.The two angles are bigger than a straight line, so they will not fit.
- Answer. No. Two obtuse angles cannot fit side by side on a straight line.
Check. Try two angles of about 100°: together they make 200°, which is more than a straight line (180°). ✓
Watch out. A straight line is exactly two right angles.