Year 5: Angles on a line, at a point and in turns
Part of the Year 5 angles and shapes chapter. Chapter overview · whole chapter on one page
Angles on a line, at a point and in turns
Angles on a straight line add up to 180°, which is a half turn. Angles at a point add up to 360°, which is a whole turn. A right angle is 90°, so 90°, 180°, 270° and 360° are all multiples of 90°.
When one angle is missing, add up the angles you know. Then take the total away to find the missing one.
Key ideas
- Angles on a straight line add up to 180°.
- Angles at a point add up to 360°.
- To find a missing angle, take the known angles away from the total.
- Multiples of 90° are 90, 180, 270 and 360.
Key words. Angles on a straight line add up to 180°, which is a half turn. Angles at a point add up to 360°, which is a whole turn.
Method. Add the known angles on a straight line, then take them away from 180.
- Add the parts we know. The angles on a straight line that we know are 65.65
- Take this away from 180. The angles on a straight line add up to 180, so the missing one is what is left.180 − 65 = 115
- Write the answer. 115°
Check. 65 + 115 = 180. ✓
Watch out. Do not add the missing part to the total. Take the known parts away from the total.
Key words. Angles on a straight line add up to 180°, which is a half turn. Angles at a point add up to 360°, which is a whole turn.
Method. Add the known angles at a point, then take them away from 360.
- Add the parts we know. The angles at a point that we know are 120 + 95.120 + 95 = 215
- Take this away from 360. The angles at a point add up to 360, so the missing one is what is left.360 − 215 = 145
- Write the answer. 145°
Check. 215 + 145 = 360. ✓
Watch out. Do not add the missing part to the total. Take the known parts away from the total.
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. Each quarter turn is a right angle, so multiply the number of quarter turns by 90.
- Count the quarter turns. A whole turn is four quarter turns.3 quarter turns
- Multiply by 90°. Each quarter turn is a right angle, which is 90°.3 × 90 = 270
- Write the answer. 270°
Check. 270 ÷ 90 = 3. ✓
Watch out. A right angle is 90°, not 9° or 100°.
Watch out
A common mistake is to think that angles on a straight line are 90° each, or that angles at a point add up to 180°. Check the total first: 180° for a straight line, 360° for a point.
Exercise 9D Missing angles on lines and at points
Non-calculatorKey words. Angles on a straight line add up to 180°, which is a half turn. Angles at a point add up to 360°, which is a whole turn.
Method. Add the known angles on a straight line, then take them away from 180.
- Add the parts we know. The angles on a straight line that we know are 70.70
- Take this away from 180. The angles on a straight line add up to 180, so the missing one is what is left.180 − 70 = 110
- Write the answer. 110°
Check. 70 + 110 = 180. ✓
Watch out. Do not add the missing part to the total. Take the known parts away from the total.
Key words. Angles on a straight line add up to 180°, which is a half turn. Angles at a point add up to 360°, which is a whole turn.
Method. Add the known angles on a straight line, then take them away from 180.
- Add the parts we know. The angles on a straight line that we know are 125.125
- Take this away from 180. The angles on a straight line add up to 180, so the missing one is what is left.180 − 125 = 55
- Write the answer. 55°
Check. 125 + 55 = 180. ✓
Watch out. Do not add the missing part to the total. Take the known parts away from the total.
Key words. Angles on a straight line add up to 180°, which is a half turn. Angles at a point add up to 360°, which is a whole turn.
Method. Add the known angles on a straight line, then take them away from 180.
- Add the parts we know. The angles on a straight line that we know are 90.90
- Take this away from 180. The angles on a straight line add up to 180, so the missing one is what is left.180 − 90 = 90
- Write the answer. 90°
Check. 90 + 90 = 180. ✓
Watch out. Do not add the missing part to the total. Take the known parts away from the total.
Key words. Angles on a straight line add up to 180°, which is a half turn. Angles at a point add up to 360°, which is a whole turn.
Method. Add the known angles on a straight line, then take them away from 180.
- Add the parts we know. The angles on a straight line that we know are 36.36
- Take this away from 180. The angles on a straight line add up to 180, so the missing one is what is left.180 − 36 = 144
- Write the answer. 144°
Check. 36 + 144 = 180. ✓
Watch out. Do not add the missing part to the total. Take the known parts away from the total.
Key words. Angles on a straight line add up to 180°, which is a half turn. Angles at a point add up to 360°, which is a whole turn.
Method. Add the known angles at a point, then take them away from 360.
- Add the parts we know. The angles at a point that we know are 150 + 90.150 + 90 = 240
- Take this away from 360. The angles at a point add up to 360, so the missing one is what is left.360 − 240 = 120
- Write the answer. 120°
Check. 240 + 120 = 360. ✓
Watch out. Do not add the missing part to the total. Take the known parts away from the total.
Key words. Angles on a straight line add up to 180°, which is a half turn. Angles at a point add up to 360°, which is a whole turn.
Method. Add the known angles at a point, then take them away from 360.
- Add the parts we know. The angles at a point that we know are 45 + 135 + 90.45 + 135 + 90 = 270
- Take this away from 360. The angles at a point add up to 360, so the missing one is what is left.360 − 270 = 90
- Write the answer. 90°
Check. 270 + 90 = 360. ✓
Watch out. Do not add the missing part to the total. Take the known parts away from the total.
Key words. Angles on a straight line add up to 180°, which is a half turn. Angles at a point add up to 360°, which is a whole turn.
Method. Add the known angles at a point, then take them away from 360.
- Add the parts we know. The angles at a point that we know are 100 + 100 + 100.100 + 100 + 100 = 300
- Take this away from 360. The angles at a point add up to 360, so the missing one is what is left.360 − 300 = 60
- Write the answer. 60°
Check. 300 + 60 = 360. ✓
Watch out. Do not add the missing part to the total. Take the known parts away from the total.
Key words. Angles on a straight line add up to 180°, which is a half turn. Angles at a point add up to 360°, which is a whole turn.
Method. Add the known angles on a straight line, then take them away from 180.
- Add the parts we know. The angles on a straight line that we know are 125.125
- Take this away from 180. The angles on a straight line add up to 180, so the missing one is what is left.180 − 125 = 55
- Write the answer. 55°
Check. 125 + 55 = 180. ✓
Watch out. Do not add the missing part to the total. Take the known parts away from the total.
Key words. Angles on a straight line add up to 180°, which is a half turn. Angles at a point add up to 360°, which is a whole turn.
Method. Add the known angles on a straight line, then take them away from 180.
- Add the parts we know. The angles on a straight line that we know are 30.30
- Take this away from 180. The angles on a straight line add up to 180, so the missing one is what is left.180 − 30 = 150
- Write the answer. 150°
Check. 30 + 150 = 180. ✓
Watch out. Do not add the missing part to the total. Take the known parts away from the total.
Key words. Angles on a straight line add up to 180°, which is a half turn. Angles at a point add up to 360°, which is a whole turn.
Method. Add the known angles at a point, then take them away from 360.
- Add the parts we know. The angles at a point that we know are 100 + 85 + 60.100 + 85 + 60 = 245
- Take this away from 360. The angles at a point add up to 360, so the missing one is what is left.360 − 245 = 115
- Write the answer. 115°
Check. 245 + 115 = 360. ✓
Watch out. Do not add the missing part to the total. Take the known parts away from the total.
Key words. Angles on a straight line add up to 180°, which is a half turn. Angles at a point add up to 360°, which is a whole turn.
Method. Add the known angles at a point, then take them away from 360.
- Add the parts we know. The angles at a point that we know are 120 + 50 + 60.120 + 50 + 60 = 230
- Take this away from 360. The angles at a point add up to 360, so the missing one is what is left.360 − 230 = 130
- Write the answer. 130°
Check. 230 + 130 = 360. ✓
Watch out. Do not add the missing part to the total. Take the known parts away from the total.
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 half turn is half of a full turn, and a full turn is 360°.a half turn = 180°
- Write the answer. 180°
Check. 180 is the right number for a half 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 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 quarter turn is a quarter of a full turn.a quarter turn = 90°
- Write the answer. 90°
Check. 90 is the right number for a quarter 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 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. Each quarter turn is a right angle, so multiply the number of quarter turns by 90.
- Count the quarter turns. A whole turn is four quarter turns.3 quarter turns
- Multiply by 90°. Each quarter turn is a right angle, which is 90°.3 × 90 = 270
- Write the answer. 270°
Check. 270 ÷ 90 = 3. ✓
Watch out. A right angle is 90°, not 9° or 100°.
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. Each quarter turn is a right angle, so multiply the number of quarter turns by 90.
- Count the quarter turns. A whole turn is four quarter turns.1 quarter turn
- Multiply by 90°. Each quarter turn is a right angle, which is 90°.1 × 90 = 90
- Write the answer. 90°
Check. 90 ÷ 90 = 1. ✓
Watch out. A right angle is 90°, not 9° or 100°.
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. Each quarter turn is a right angle, so multiply the number of quarter turns by 90.
- Count the quarter turns. A whole turn is four quarter turns.2 quarter turns
- Multiply by 90°. Each quarter turn is a right angle, which is 90°.2 × 90 = 180
- Write the answer. 180°
Check. 180 ÷ 90 = 2. ✓
Watch out. A right angle is 90°, not 9° or 100°.
Key words. Angles on a straight line add up to 180°, which is a half turn. Angles at a point add up to 360°, which is a whole turn.
Method. Add the known turns, then take them away from 360.
- Add the parts we know. The turns that we know are 270.270
- Take this away from 360. The turns add up to 360, so the missing one is what is left.360 − 270 = 90
- Write the answer. 90°
Check. 270 + 90 = 360. ✓
Watch out. Do not add the missing part to the total. Take the known parts away from the total.
Key words. Angles on a straight line add up to 180°, which is a half turn. Angles at a point add up to 360°, which is a whole turn.
Method. Add the two angles, then think of other sizes that also work.
- Add the two angles. Angles on a straight line add up to 180°.90 + 90 = 180
- Try other sizes. Two angles on a straight line can be 60° and 120°, and these also add up to 180°.60 + 120 = 180
- Decide. Sam is right only in the special case when both angles are 90°.Sometimes
Check. 90 + 90 = 180, and 60 + 120 = 180 too. ✓
Watch out. One example that works does not prove that something is always true.
Key words. Angles on a straight line add up to 180°, which is a half turn. Angles at a point add up to 360°, which is a whole turn.
Method. Add up the four angles, then try different sizes.
- Add four right angles. Four angles of 90° add up to 360°.4 × 90 = 360
- Try four different angles. Angles at a point do not all have to be equal.100 + 80 + 120 + 60 = 360
- Decide. So Tom is wrong. The four angles only need to add up to 360°.No
Check. Both sets add up to 360°. ✓
Watch out. The total must be 360°. The sizes of the angles can be different.
Key words. Angles on a straight line add up to 180°, which is a half turn. Angles at a point add up to 360°, which is a whole turn.
Method. Pick four angles that add up to 360°, in two different ways.
- First set. Four right angles.90 + 90 + 90 + 90
- Second set. Four different angles, added together.100 + 80 + 120 + 60
- Check the answer. Both sets add up to the total for a point.Both totals are 360
Check. 90 + 90 + 90 + 90 = 360 and 100 + 80 + 120 + 60 = 360. ✓
Watch out. Check the total of each set. A set that adds up to 350 is not right.