Geometry and proof · Ages 12–13

Vertically opposite angles worksheet

Part of: Angles & parallel lines

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Geometry and proof · Ages 12–13

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Name:Date:Score:／48

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

1.Two straight lines cross, as shown. x =
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2.Two straight lines cross, as shown. x =
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3.Two straight lines cross, as shown. x = °, y = °, z = °.
Fill in each blank
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4.Three straight lines meet at a point, as shown. x =
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5.Two straight lines cross, and a ray splits one of the angles into two equal angles x, as shown. x =
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6.Two straight lines cross, as shown, and the two angles marked a add up to 252°. x =
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7.Two straight lines cross, as shown, and the two angles marked a add up to 294°. x =
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8.Two straight lines cross, as shown, and the two angles marked a add up to 160°. x =
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9.Two straight lines cross, as shown. Which statement is right?
- A. x = 50° (vert. opp. ∠s)
- B. x = 130° (adj. ∠s on st. line)
- C. x = 130° (vert. opp. ∠s)
- D. x = 50° (adj. ∠s on st. line)
Choose the right answer
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10.Two straight lines cross, and one angle is 73°. The angle opposite it is 73°.
True or false?
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11.Two straight lines cross, and one angle is 140°. The angle opposite it is 140°.
True or false?
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12.Two straight lines cross, and one angle is 23°. The angle opposite it is 23°.
True or false?
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13.A pair of scissors is open, its two blades 50° apart. What is the angle between the two handles?
Working:
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14.Two straight roads cross at a slant, one angle 151°. What do the other three angles add up to?
Working:
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15.Two straight lines cross. Two angles side by side are in the ratio 1 : 2. The smaller = °, the larger = °.
Fill in each blank
Working:
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16.Three straight lines meet at a point, as shown. Find x: put the steps in order.
- A. x = 180° − 73° − 67° = 40°
- B. x + 73° + y = 180° (adj. ∠s on st. line)
- C. y = 67° (vert. opp. ∠s)
Write the letters in the right order
Working:
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17.Two straight roads cross in an X. One angle is 68° more than the angle next to it. What is the larger angle?
Working:
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18.Three straight lines meet at a point, as shown. x = 180° − 74° − 51° = ° (adj. ∠s on st. line), y = x = ° (vert. opp. ∠s).
Fill in each blank
Working:
Answer:

Show the answers and working

Vertically opposite angles worksheet: Answers and working

1. 89°
x faces 89° across the crossing, so they are vertically opposite: x = 89° (vert. opp. ∠s).
2. 70°
x and 110° sit side by side on one straight line: x = 180° − 110° = 70° (adj. ∠s on st. line).
3. 54, 126, 54
x = 180° − 126° = 54° (adj. ∠s on st. line); y faces 126°, so y = 126° (vert. opp. ∠s); z faces x, so z = 54° (vert. opp. ∠s).
4. 58°
The angle opposite 73° lies on one straight line with 49° and x: x = 180° − 73° − 49° = 58° (vert. opp. ∠s, adj. ∠s on st. line).
5. 35°
The angle split in two lies on a straight line with 110°: 180° − 110° = 70° (adj. ∠s on st. line). It splits into two equal parts: x = 70° ÷ 2 = 35°.
6. 54°
The two a are vertically opposite, so equal (vert. opp. ∠s): a = 252° ÷ 2 = 126°. x and a lie on a straight line: x = 180° − 126° = 54° (adj. ∠s on st. line).
7. 33°
The two a are vertically opposite, so equal (vert. opp. ∠s): a = 294° ÷ 2 = 147°. x and a lie on a straight line: x = 180° − 147° = 33° (adj. ∠s on st. line).
8. 100°
The two a are vertically opposite, so equal (vert. opp. ∠s): a = 160° ÷ 2 = 80°. x and a lie on a straight line: x = 180° − 80° = 100° (adj. ∠s on st. line).

9. D. x = 50° (adj. ∠s on st. line)
Two angles facing each other are vertically opposite and equal; two side by side lie on a straight line and add to 180°. Here x = 50°.
10. True
Opposite angles are equal: the one opposite 73° is 73° too (vert. opp. ∠s); the two beside it are 180° − 73° = 107° (adj. ∠s on st. line).
11. True
Opposite angles are equal: the one opposite 140° is 140° too (vert. opp. ∠s); the two beside it are 180° − 140° = 40° (adj. ∠s on st. line).
12. True
Opposite angles are equal: the one opposite 23° is 23° too (vert. opp. ∠s); the two beside it are 180° − 23° = 157° (adj. ∠s on st. line).

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

13. 50°
Blades and handles are two crossing straight lines; the blades' angle and the handles' face each other, so they are vertically opposite: also 50°.
14. 209°
The four go round the crossing and add to 360° (∠s at a pt.): 360° − 151° = 209°. Or one by one: the opposite angle is 151°, the other two 29° each, and 151 + 29 + 29 = 209.
15. 60, 120
Angles side by side add to 180° (adj. ∠s on st. line): 1 + 2 parts of 60°, so 60° and 120°. The other two are their opposite angles, 60° and 120° again.
16. C → B → A
y faces 67°, so y = 67°; 73°, y and x lie along one straight line, so x = 180° − 73° − 67° = 40°.
17. 124°
Angles side by side add to 180° (adj. ∠s on st. line). With y the smaller: y + (y + 68) = 180, y = 56, so the larger is 124°.
18. 55, 55
74°, 51° and x together lie along one straight line: x = 180° − 74° − 51° = 55°. y faces x, so they are vertically opposite: y = 55°.

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