Shape and space · Ages 9–10

Measuring angles in degrees worksheet

Part of: Quadrilaterals, tiling and the eight directions

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Shape and space · Ages 9–10

Numsprite
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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.A protractor measures ∠AOB. How many degrees is ∠AOB?
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2.The angles in the picture are on a straight line. What is the angle marked ? in degrees?
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3.A protractor measures ∠AOB. How many degrees is ∠AOB?
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4.The angles in the picture are all round one point. What is the angle marked ? in degrees?
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5.The angles in the picture are all round one point. What is the angle marked ? in degrees?
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13.The 12 numbers on a clock face split a whole turn into 12 equal parts. The hour hand moves from 12 to 4. How many degrees does it turn?
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14.Ka-yan cuts a round pizza from its centre into 12 equal slices. How many degrees is the angle at the tip of each slice?
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15.Ka-lok stands facing north and turns 230° to the right. How many more degrees to the right must Ka-lok turn to make exactly one whole turn?
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16.One end of a seesaw rests on the flat ground, and the plank makes two angles with the ground there. One is 10°. How many degrees is the other?
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17.Ming stands facing north and turns 230° to the right. How many more degrees to the right must Ming turn to make exactly one whole turn?
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18.May cuts a round pizza from its centre into 3 equal slices. How many degrees is the angle at the tip of each slice?
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Show the answers and working

Measuring angles in degrees worksheet: Answers and working

1. 120°
First see which 0° OA lies on, then decide whether to read the inner ring or the outer one.
OA is on the 0° at the right, so read the inner ring: OB points at 120, ∠AOB = 120°.
2. 115°
The angles are on a straight line, so together they make 180°. Find the angle you already know first.
Angles on a straight line make 180°: 180 − 65 = 115.
3. 130°
OA lies on the 0° at the left. Reading from that 0°, which ring should you use?
OA is on the 0° at the left, so read the outer ring: OB points at 130, ∠AOB = 130° (the inner 50 is the other angle).
4. 165°
Angles round a point make 360°. Add the two angles you already know first.
Angles round a point make 360°: 80 + 115 = 195, and 360 − 195 = 165.
5. 175°
Angles round a point make 360°. Add the three angles you already know first.
Add the known angles: 55 + 80 + 50 = 185; round a point is 360°: 360 − 185 = 175.

6. D. 160°
See which 0° OA lies on and read that ring; then compare the angle with a right angle.
Read from the 0° on OA's side: OB points at 160, ∠AOB = 160°. Compare with a right angle to see that it makes sense.
7. False
See which 0° OA lies on, then check whether 50° is read from that ring.
Reading from the 0° on OA's side, ∠AOB = 130°; first see whether it is bigger or smaller than a right angle.
8. True
See which 0° OA lies on, then check whether 150° is read from that ring.
Reading from the 0° on OA's side, ∠AOB = 150°; first see whether it is bigger or smaller than a right angle.
9. False
See which 0° OA lies on, then check whether 120° is read from that ring.
Reading from the 0° on OA's side, ∠AOB = 60°; first see whether it is bigger or smaller than a right angle.
10. True
See which 0° OA lies on, then check whether 30° is read from that ring.
Reading from the 0° on OA's side, ∠AOB = 30°; first see whether it is bigger or smaller than a right angle.
11. False
See which 0° OA lies on, then check whether 20° is read from that ring.
Reading from the 0° on OA's side, ∠AOB = 160°; first see whether it is bigger or smaller than a right angle.
12. True
See which 0° OA lies on, then check whether 100° is read from that ring.
Reading from the 0° on OA's side, ∠AOB = 100°; first see whether it is bigger or smaller than a right angle.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 120°
A whole turn is 360°, split into 12 equal parts. Work out one part first.
A whole turn is 360°, so each part is 360 ÷ 12 = 30°; 4 parts: 30 × 4 = 120.
14. 30°
The angles round the centre make 360°, shared equally among 12 slices.
The angles round the centre make 360°: 360 ÷ 12 = 30.
15. 130°
How many degrees is a whole turn? Ka-lok has turned 230° already; how much is left?
A whole turn is 360°: 360 − 230 = 130.
16. 170°
The ground is a straight line. What do the two angles on a line add up to?
The ground is a straight line, and angles on a line make 180°: 180 − 10 = 170.
17. 130°
How many degrees is a whole turn? Ming has turned 230° already; how much is left?
A whole turn is 360°: 360 − 230 = 130.
18. 120°
The angles round the centre make 360°, shared equally among 3 slices.
The angles round the centre make 360°: 360 ÷ 3 = 120.

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