Geometry and proof · Ages 12–13

Angles on a line and at a point worksheet

Part of: Angles & parallel lines

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Geometry and proof · Ages 12–13

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

1.The angles are all round one point. x =
Answer:
2.The three angles lie on a straight line. x + 64° + 54° = °, x = °.
Fill in each blank
Answer:
3.The two angles lie on a straight line. x =
Answer:
4.The four angles go round one point. x =
Answer:
5.The four angles go round one point, and the three marked x are equal. x =
Answer:
6.The three angles lie on a straight line, and the two marked x are equal. x =
Answer:
7.The four angles go round one point, and the two marked x are equal. x =
Answer:

8.Two angles are 41° and 139°. They can be adjacent angles on a straight line.
True or false?
Answer:
9.Which reason finds x in the picture?
- A. vert. opp. ∠s
- B. ∠ sum of △
- C. adj. ∠s on st. line
- D. ∠s at a pt.
Choose the right answer
Answer:
10.Two angles are 48° and 312°. They can be adjacent angles on a straight line.
True or false?
Answer:
11.Three angles are 94°, 114° and 142°. They can be all the angles round one point.
True or false?
Answer:
12.Three angles are 115°, 105° and 150°. They can be all the angles round one point.
True or false?
Answer:

13.x = 360° − 112° − 88° = 160° (______). Which reason goes in the blank?
- A. vert. opp. ∠s
- B. ∠s at a pt.
- C. adj. ∠s on st. line
- D. ∠ sum of △
Choose the right answer
Working:
Answer:
14.At 8 o'clock, what is the smaller angle between the hour hand and the minute hand?
Working:
Answer:
15.A wheel has 6 spokes spread evenly out from its centre. What is the angle between two spokes side by side?
Working:
Answer:
16.The two angles lie on a straight line. x = 180° − 52° = 128° (______). Which reason goes in the blank?
- A. adj. ∠s on st. line
- B. vert. opp. ∠s
- C. ∠s at a pt.
- D. ∠ sum of △
Choose the right answer
Working:
Answer:
17.AOB is a straight line. A ray OC splits it into ∠AOC and ∠COB in the ratio 1 : 2. ∠AOC = °, ∠COB = °.
Fill in each blank
Working:
Answer:
18.The three angles marked x are equal. Find x: put the steps in order.
- A. 3x = 264°
- B. x = 88°
- C. 3x + 96° = 360° (∠s at a pt.)
Write the letters in the right order
Working:
Answer:

Show the answers and working

Angles on a line and at a point worksheet: Answers and working

1. 202°
x + 64° + 94° = 360° (∠s at a pt.), x = 360° − 64° − 94° = 202°.
2. 180, 62
Angles on a straight line add to 180°: x + 64° + 54° = 180° (adj. ∠s on st. line), x = 180° − 64° − 54° = 62°.
3. 33°
x + 147° = 180° (adj. ∠s on st. line), x = 180° − 147° = 33°.
4. 46°
x + 119° + 105° + 90° = 360° (∠s at a pt.), so x = 360° − 119° − 105° − 90° = 46°. The right angle counts too.
5. 97°
x + x + x + 69° = 360° (∠s at a pt.), 3x = 360° − 69° = 291°, x = 97°.
6. 65°
x + x + 50° = 180° (adj. ∠s on st. line), 2x = 180° − 50° = 130°, x = 65°.
7. 75°
x + x + 122° + 88° = 360° (∠s at a pt.), 2x = 360° − 122° − 88° = 150°, x = 75°.

8. True
Adjacent angles on a straight line add to 180° (adj. ∠s on st. line). 41° + 139° = 180°, and it must be 180°.
9. C. adj. ∠s on st. line
Angles on a straight line add to 180° (adj. ∠s on st. line); angles round a point add to 360° (∠s at a pt.). Here x = 51°.
10. False
Adjacent angles on a straight line add to 180° (adj. ∠s on st. line). 48° + 312° = 360°, and it must be 180°.
11. False
All the angles round a point add to 360° (∠s at a pt.). 94° + 114° + 142° = 350°, and it must be 360°.
12. False
All the angles round a point add to 360° (∠s at a pt.). 115° + 105° + 150° = 370°, and it must be 360°.

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

13. B. ∠s at a pt.
x, 112° and 88° go round one point and make a full turn, 360°: the reason is ∠s at a pt.
14. 120°
A full turn of the face is 360°, in 12 spaces of 360° ÷ 12 = 30°. At 8 o'clock the hands are 8 spaces apart: 8 × 30° = 240°; over 180°, the smaller angle is 360° minus that. The answer is 120°.
15. 60°
6 equal angles go round the centre and add to 360° (∠s at a pt.): 360° ÷ 6 = 60°.
16. A. adj. ∠s on st. line
x and 52° are side by side on one straight line and add to 180°: the reason is adj. ∠s on st. line.
17. 60, 120
The two add to 180° (adj. ∠s on st. line): 1 + 2 parts, 60° each. ∠AOC = 1 × 60° = 60°, ∠COB = 2 × 60° = 120°.
18. C → A → B
The four angles go round a point and add to 360°: 3x + 96° = 360°, 3x = 264°, x = 88°.

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