Shape and space · Ages 11–12

The protractor and naming angles worksheet

Part of: Angles

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Shape and space · Ages 11–12

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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 the angle. How many degrees is ∠AOB?
Answer:
2.∠AOB = 60°. How many degrees is the reflex angle marked?
Answer:
3.A protractor measures the angle. How many degrees is ∠AOB?
Answer:
4.∠AOB = 115°. How many degrees is the reflex angle marked?
Answer:
5.A protractor measures the angle, but neither arm is on 0°. How many degrees is ∠AOB?
Answer:

6.What kind of angle is 215°?
- A. Obtuse
- B. Straight
- C. Reflex
- D. Acute
Choose the right answer
Answer:
7.What kind of angle is 160°?
- A. Reflex
- B. Straight
- C. Obtuse
- D. Acute
Choose the right answer
Answer:
8.Which angle is marked in the picture?
- A. ∠CDA
- B. ∠BCD
- C. ∠ABC
- D. ∠DAB
Choose the right answer
Answer:
9.Estimate: about how many degrees is ∠AOB?
- A. 90
- B. 100
- C. 140
- D. 80
Choose the right answer
Answer:
10.Drawing a 50° angle with a protractor: the centre on the corner, one arm on the inner 0°, then a dot at 130° on the inner scale, joined to the corner.
True or false?
Answer:
11.Drawing a 55° angle with a protractor: the centre on the corner, one arm on the inner 0°, then a dot at 55° on the inner scale, joined to the corner.
True or false?
Answer:
12.Drawing a 105° angle with a protractor: the centre on the corner, one arm on the inner 0°, then a dot at 75° on the inner scale, joined to the corner.
True or false?
Answer:

13.A door is opened 55° from shut, then 45° more. How many more degrees must it open to make a straight angle with where it started?
Working:
Answer:
14.A folding fan opens to an angle of 180°, and its ribs split it into 6 equal parts. How many degrees is each part?
Working:
Answer:
15.A round pizza is cut from the centre into 9 equal slices. How many degrees is each slice's angle at the centre?
Working:
Answer:
16.A clock's minute hand points at 12 and its hour hand at 3. How many degrees is the smaller angle between the hands?
Working:
Answer:
17.Chi-keung faces north, turns 135° clockwise, then 105° more. Chi-keung has turned ° in all, and needs ° more to make a full turn.
Fill in each blank
Working:
Answer:
18.A round pizza is cut from the centre into 8 equal slices. How many degrees is each slice's angle at the centre?
Working:
Answer:

Show the answers and working

The protractor and naming angles worksheet: Answers and working

1. 145°
Which side's 0° is OA on? Read from that scale's 0° and see where OB points.
OA is on the 0° at the right, so read the inner scale: OB points at 145, ∠AOB = 145°.
2. 300°
The reflex angle and the 60° angle make a full turn. How many degrees is that?
The two angles make a full turn of 360°: 360 − 60 = 300.
3. 30°
OA is on the 0° at the left. Is that the inner or outer scale? Read that same scale.
OA is on the 0° at the left, so read the outer scale: OB points at 30, ∠AOB = 30° (the inner 150 belongs to the other angle).
4. 245°
The reflex angle and the 115° angle make a full turn. How many degrees is that?
The two angles make a full turn of 360°: 360 − 115 = 245.
5. 60°
Neither arm is on 0°. Read OA and OB on the same scale first, then find the difference.
Take one reading from the other on the same scale: inner OB 100, OA 40, 100 − 40 = 60°.

6. C. Reflex
Is 215° more or less than 90°? And than 180°?
Compare with 90°, 180° and 360°: acute < 90° < obtuse < 180° (straight) < reflex < 360°.
7. C. Obtuse
Is 160° more or less than 90°? And than 180°?
Compare with 90°, 180° and 360°: acute < 90° < obtuse < 180° (straight) < reflex < 360°.
8. D. ∠DAB
First see which corner the marked angle is at; that letter goes in the middle of the name.
The middle letter of an angle's name is its corner: see which corner is marked.
9. D. 80
Compare it with a right angle first: more or less than 90°? Then judge by how much.
Compare it with a right angle (90°) first, then judge how far from one it is: about 80°.
10. False
With the arm on the inner 0°, which scale should you count 50° on? Then check 130.
With the arm on the inner 0°, count to 50° on that same scale.
11. True
With the arm on the inner 0°, which scale should you count 55° on? Then check 55.
With the arm on the inner 0°, count to 55° on that same scale.
12. False
With the arm on the inner 0°, which scale should you count 105° on? Then check 75.
With the arm on the inner 0°, count to 105° on that same scale.

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

13. 80°
A straight angle is 180°. First find how far it has opened: 55 + 45.
A straight angle is 180°: 55 + 45 = 100° so far, 180 − 100 = 80°.
14. 30°
The whole fan is 180°, split equally into 6, so divide.
180 ÷ 6 = 30°.
15. 40°
How many degrees are there all round the centre? Share them into 9.
All the way round the centre is 360°: 360 ÷ 9 = 40°.
16. 90°
A clock face's 360° is split into 12 equal gaps. The minute hand is on 12 and the hour hand on 3: how many gaps apart?
Neighbouring numbers on a clock are 360° ÷ 12 = 30° apart; the gaps between the hands × 30°, the smaller way round: 90°.
17. 240, 120
Add the two turns first; a full turn is 360°.
135 + 105 = 240; a full turn is 360°: 360 − 240 = 120.
18. 45°
How many degrees are there all round the centre? Share them into 8.
All the way round the centre is 360°: 360 ÷ 8 = 45°.

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