Year 5: Measuring angles in degrees
Part of the Year 5 angles and shapes chapter. Chapter overview · whole chapter on one page
Measuring angles in degrees
An angle is the amount of turn between two lines that meet at a point. We measure angles in degrees, using the symbol °. A full turn is 360°. A half turn is 180°. A quarter turn is 90°, and a quarter turn is a right angle.
| Type | Size | What it looks like |
|---|---|---|
| Acute | less than 90° | a sharp, narrow corner |
| Right | exactly 90° | a square corner, like the corner of a book |
| Obtuse | more than 90° but less than 180° | wider than a corner, but not flat |
| Reflex | more than 180° but less than 360° | the big outside of a turn |
Key ideas
- An acute angle is less than 90°.
- A right angle is exactly 90°.
- An obtuse angle is more than 90° and less than 180°.
- A reflex angle is more than 180° and less than 360°.
- Estimate an angle by comparing it with a right angle, and a straight line.
Key words. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A reflex angle is more than 180° and less than 360°.
Method. Compare the size of the angle with 90°, 180° and 360° to find its type.
- Compare the angle with a right angle. A right angle is 90°.115° > 90°
- Compare the angle with a straight line. A straight line is 180°.115° < 180°
- Name the type of angle. An angle more than 90° and less than 180° is obtuse.obtuse
- Write the answer. So the angle 115° is obtuse.obtuse
Check. 115° is between 90° and 180°, so it is obtuse. ✓
Watch out. Look at the number of degrees, not at how long the arms look.
Key words. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A reflex angle is more than 180° and less than 360°.
Method. Compare the size of the angle with 90°, 180° and 360° to find its type.
- Compare the angle with a straight line. A straight line is 180°.260° > 180°
- Compare the angle with a full turn. A full turn is 360°.260° < 360°
- Name the type of angle. An angle more than 180° and less than 360° is reflex.reflex
- Write the answer. So the angle 260° is reflex.reflex
Check. 260° is between 180° and 360°, so it is reflex. ✓
Watch out. Look at the number of degrees, not at how long the arms look.
Key words. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A reflex angle is more than 180° and less than 360°.
Method. Compare 180° with the types of angle.
- Compare with a right angle. An obtuse angle is bigger than 90°.180° > 90°
- Compare with a straight line. An obtuse angle must be smaller than 180°. A straight line is exactly 180°.180° is not less than 180°
- Write the answer. An angle of exactly 180° is a straight line, not an obtuse angle.No, 180° is a straight angle
Check. Obtuse angles are less than 180°, so 180° cannot be obtuse. ✓
Watch out. 180° is a straight line, so it is not obtuse.
Watch out
A common mistake is to judge an angle by how long its arms look. Only the number of degrees matters. Also, 180° is not obtuse: it is a straight line.
Exercise 9B Acute, right, obtuse and reflex angles
Non-calculatorKey words. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A reflex angle is more than 180° and less than 360°.
Method. Compare the size of the angle with 90°, 180° and 360° to find its type.
- Compare the angle with a right angle. A right angle is 90°.35° < 90°
- Name the type of angle. An angle less than 90° is acute.acute
- Write the answer. So the angle 35° is acute.acute
Check. 35° is less than 90°, so it is acute. ✓
Watch out. Look at the number of degrees, not at how long the arms look.
Key words. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A reflex angle is more than 180° and less than 360°.
Method. Compare the size of the angle with 90°, 180° and 360° to find its type.
- Compare the angle with a right angle. A right angle is exactly 90°.90° = 90°
- Name the type of angle. An angle of exactly 90° is a right angle.right
- Write the answer. So the angle 90° is right.right
Check. A right angle is 90°, and this angle is 90°. ✓
Watch out. Look at the number of degrees, not at how long the arms look.
Key words. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A reflex angle is more than 180° and less than 360°.
Method. Compare the size of the angle with 90°, 180° and 360° to find its type.
- Compare the angle with a right angle. A right angle is 90°.118° > 90°
- Compare the angle with a straight line. A straight line is 180°.118° < 180°
- Name the type of angle. An angle more than 90° and less than 180° is obtuse.obtuse
- Write the answer. So the angle 118° is obtuse.obtuse
Check. 118° is between 90° and 180°, so it is obtuse. ✓
Watch out. Look at the number of degrees, not at how long the arms look.
Key words. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A reflex angle is more than 180° and less than 360°.
Method. Compare the size of the angle with 90°, 180° and 360° to find its type.
- Compare the angle with a straight line. A straight line is 180°.200° > 180°
- Compare the angle with a full turn. A full turn is 360°.200° < 360°
- Name the type of angle. An angle more than 180° and less than 360° is reflex.reflex
- Write the answer. So the angle 200° is reflex.reflex
Check. 200° is between 180° and 360°, so it is reflex. ✓
Watch out. Look at the number of degrees, not at how long the arms look.
Key words. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A reflex angle is more than 180° and less than 360°.
Method. Compare the size of the angle with 90°, 180° and 360° to find its type.
- Compare the angle with a straight line. A straight line is 180°.310° > 180°
- Compare the angle with a full turn. A full turn is 360°.310° < 360°
- Name the type of angle. An angle more than 180° and less than 360° is reflex.reflex
- Write the answer. So the angle 310° is reflex.reflex
Check. 310° is between 180° and 360°, so it is reflex. ✓
Watch out. Look at the number of degrees, not at how long the arms look.
Key words. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A reflex angle is more than 180° and less than 360°.
Method. Compare the size of the angle with 90°, 180° and 360° to find its type.
- Compare the angle with a right angle. A right angle is 90°.179° > 90°
- Compare the angle with a straight line. A straight line is 180°.179° < 180°
- Name the type of angle. An angle more than 90° and less than 180° is obtuse.obtuse
- Write the answer. So the angle 179° is obtuse.obtuse
Check. 179° is between 90° and 180°, so it is obtuse. ✓
Watch out. Look at the number of degrees, not at how long the arms look.
Key words. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A reflex angle is more than 180° and less than 360°.
Method. Compare the size of the angle with 90°, 180° and 360° to find its type.
- Compare the angle with a right angle. A right angle is 90°.60° < 90°
- Name the type of angle. An angle less than 90° is acute.acute
- Write the answer. So the angle 60° is acute.acute
Check. 60° is less than 90°, so it is acute. ✓
Watch out. Look at the number of degrees, not at how long the arms look.
Key words. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A reflex angle is more than 180° and less than 360°.
Method. Compare the size of the angle with 90°, 180° and 360° to find its type.
- Compare the angle with a right angle. A right angle is 90°.150° > 90°
- Compare the angle with a straight line. A straight line is 180°.150° < 180°
- Name the type of angle. An angle more than 90° and less than 180° is obtuse.obtuse
- Write the answer. So the angle 150° is obtuse.obtuse
Check. 150° is between 90° and 180°, so it is obtuse. ✓
Watch out. Look at the number of degrees, not at how long the arms look.
Key words. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A reflex angle is more than 180° and less than 360°.
Method. Compare the size of the angle with 90°, 180° and 360° to find its type.
- Compare the angle with a straight line. A straight line is 180°.250° > 180°
- Compare the angle with a full turn. A full turn is 360°.250° < 360°
- Name the type of angle. An angle more than 180° and less than 360° is reflex.reflex
- Write the answer. So the angle 250° is reflex.reflex
Check. 250° is between 180° and 360°, so it is reflex. ✓
Watch out. Look at the number of degrees, not at how long the arms look.
Key words. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A reflex angle is more than 180° and less than 360°.
Method. Compare the angle with the three choices.
- Compare with a right angle. The arms are wider than a right angle, so the angle is more than 90°.110° > 90°
- Compare with a straight line. The arms are not as wide as a straight line, so the angle is less than 180°.110° < 180°
- Choose the best estimate. Of the three choices, 110° is the only one between 90° and 180°.110°
Check. 110° is between 90° and 180°, which matches the picture. ✓
Watch out. 40° is too small and 250° is too big for this picture.
Key words. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A reflex angle is more than 180° and less than 360°.
Method. Compare the angle with a right angle, then look at the choices.
- Compare with a right angle. The arms are much closer together than a right angle, so the angle is acute.less than 90°
- Look at the choices. Only 30° is close to this size. The choice of 300° is reflex, and 60° is too big.30° is closest
- Choose the best estimate. The arms are about one third of a right angle, so 30° is the best estimate.30°
Check. 30° is a third of a right angle, which matches. ✓
Watch out. Think of the right angle as 90° and compare with it.
Key words. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A reflex angle is more than 180° and less than 360°.
Method. Put the angles in order by their number of degrees, starting with the smallest.
- Write the angles. These are the angles we need to put in order.150°, 45°, 260°, 90°
- Compare the numbers. The smallest number is the smallest angle.45 < 90 < 150 < 260
- Write the answer, smallest first. 45°, 90°, 150°, 260°
Check. Each angle is smaller than the next one. ✓
Watch out. Do not put angles in order by how long their arms look.
Key words. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A reflex angle is more than 180° and less than 360°.
Method. Give the range for each type of angle, then compare the two ranges.
- Give the range for a reflex angle. A reflex angle is more than 180° and less than 360°.180° < reflex < 360°
- Give the range for an obtuse angle. An obtuse angle is more than 90° and less than 180°.90° < obtuse < 180°
- Compare the two ranges. Every reflex angle is more than 180°, and every obtuse angle is less than 180°.Yes, Ali is right
Check. The two ranges do not overlap, and reflex is the bigger one. ✓
Watch out. Check the numbers at the ends of each range.
Key words. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A reflex angle is more than 180° and less than 360°.
Method. Compare each angle with 90° and 180°.
- Compare each angle with 90°. We need an angle bigger than 90°.85 no, 95 yes, 180 yes, 270 yes
- Compare with 180°. We need an angle smaller than 180°.95 < 180 yes, 180 is not less
- Write the answer. 95°
Check. 95° is more than 90° and less than 180°. ✓
Watch out. The angle must be bigger than a right angle and smaller than a straight line.
Key words. An angle is the amount of turn between two lines (the arms) that meet at a point (the vertex). We measure angles in degrees, written with the symbol °.
Method. Learn these facts about turns: a right angle is 90, a half turn is 180 and a whole turn is 360.
- Recall the fact. A right angle is a quarter of a full turn.a right angle = 90°
- Write the answer. 90°
Check. 90 is the right number for a right angle. ✓
Watch out. A whole turn is bigger than a half turn, and a half turn is bigger than a right angle.
Key words. An angle is the amount of turn between two lines (the arms) that meet at a point (the vertex). We measure angles in degrees, written with the symbol °.
Method. Learn these facts about turns: a right angle is 90, a half turn is 180 and a whole turn is 360.
- Recall the fact. A straight line is a half turn.a straight line = 180°
- Write the answer. 180°
Check. 180 is the right number for a straight line. ✓
Watch out. A whole turn is bigger than a half turn, and a half turn is bigger than a right angle.
Key words. An angle is the amount of turn between two lines (the arms) that meet at a point (the vertex). We measure angles in degrees, written with the symbol °.
Method. Learn these facts about turns: a right angle is 90, a half turn is 180 and a whole turn is 360.
- Recall the fact. A full turn goes all the way round a point.a full turn = 360°
- Write the answer. 360°
Check. 360 is the right number for a full turn. ✓
Watch out. A whole turn is bigger than a half turn, and a half turn is bigger than a right angle.
Key words. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A reflex angle is more than 180° and less than 360°.
Method. Compare 90° with the ranges for each type of angle.
- Compare with a right angle. A right angle is exactly 90°.90° = 90°
- Compare with the type names. An obtuse angle must be more than 90°, so 90° is not obtuse.90° is not more than 90°
- Write the answer. No, 90° is a right angle
Check. Obtuse angles are more than 90°, so 90° is not obtuse. ✓
Watch out. A right angle is exactly 90°, and it is not obtuse.
Key words. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A reflex angle is more than 180° and less than 360°.
Method. Pick numbers in each range.
- Acute angles. Acute angles are less than 90°, so pick three numbers from 1 to 89.20°, 45°, 80°
- Obtuse angles. Obtuse angles are more than 90° and less than 180°.100°, 130°, 170°
- Check the answer. Each angle must be in the right range.Any answers in these ranges are correct.
Check. Each acute angle is less than 90°, and each obtuse angle is between 90° and 180°. ✓
Watch out. An angle of exactly 90° is right, not acute or obtuse.