Geometry and proof · Ages 12–13

Angles with parallel lines 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.

13.AB // CD and ∠AEF = 40°, as shown. ∠EFD = ∠AEF = 40° (______). Which reason goes in the blank?
- A. int. ∠s, AB // CD
- B. alt. ∠s, AB // CD
- C. vert. opp. ∠s
- D. corr. ∠s, AB // CD
Choose the right answer
Working:
Answer:
14.A slanting path crosses the two parallel edges of a pavement. On one side of the path, between the edges, it makes 86° with the upper edge. What angle does it make with the lower edge, on the same side and between the edges?
Working:
Answer:
15.AB // CD and ∠AEF = 135°, as shown. Find ∠EFC: put the steps in order.
- A. ∠EFD = ∠AEF = 135° (alt. ∠s, AB // CD)
- B. ∠EFC = 180° − 135° = 45°
- C. ∠EFC = 180° − ∠EFD (adj. ∠s on st. line)
Write the letters in the right order
Working:
Answer:
16.AB // CD, and EF cuts them at E and F. ∠AEF = (3x − 22)° and ∠EFD = (2x + 20)°. 3x − 22 = 2x + 20 (alt. ∠s, AB // CD), x = , ∠AEF = °.
Fill in each blank
Working:
Answer:
17.AB // CD and ∠AEF = 120°, as shown. ∠BEF = ° (adj. ∠s on st. line), ∠EFC = ° (alt. ∠s, AB // CD).
Fill in each blank
Working:
Answer:
18.A railing's two bars are parallel and a slanting bar cuts them, as shown. What is x?
Working:
Answer:

Show the answers and working

Angles with parallel lines worksheet: Answers and working

1. 50°
Place first: corresponding (F) and alternate (Z) angles are equal, interior ones (C) add to 180° (AB // CD). Where x is from 130° gives x = 50°.
2. 50°
x and 130° are on one side, both between the lines: interior angles. x = 180° − 130° = 50° (int. ∠s, AB // CD).
3. 120°
The angle corresponding to 60° sits beside x and is 60° too (corr. ∠s, AB // CD); it lies on CD with x, so x = 180° − 60° = 120° (adj. ∠s on st. line).
4. 55, 55, 125
x = 55° (vert. opp. ∠s); y = 55° (corr. ∠s, AB // CD); z sits beside y on CD: z = 180° − 55° = 125° (adj. ∠s on st. line).
5. 75°
The angle corresponding to 75° is vertically opposite x: it is 75° (corr. ∠s, AB // CD), so x = 75° (vert. opp. ∠s).
6. 18
The two are on opposite sides, both between AB and CD: alternate angles, so equal. 2x + 14 = 4x − 22 (alt. ∠s, AB // CD), 2x = 36, x = 18.

7. D. alt. ∠s, AB // CD
x and 40° are on opposite sides, both between AB and CD (a Z): alternate angles. AB // CD, so x = 40° (alt. ∠s, AB // CD).
8. C. alt. ∠s, AB // CD
x and 105° are on opposite sides, both between AB and CD (a Z): alternate angles. AB // CD, so x = 105° (alt. ∠s, AB // CD).
9. D. alt. ∠s, AB // CD
x and 115° are on opposite sides, both between AB and CD (a Z): alternate angles. AB // CD, so x = 115° (alt. ∠s, AB // CD).
10. True
Corresponding and alternate angles are equal, interior ones add to 180° (AB // CD). Whether x is 50° or 180° − 50° depends on where it is: x = 130°.
11. True
Corresponding and alternate angles are equal, interior ones add to 180° (AB // CD). Whether x is 110° or 180° − 110° depends on where it is: x = 70°.
12. False
Corresponding and alternate angles are equal, interior ones add to 180° (AB // CD). Whether x is 75° or 180° − 75° depends on where it is: x = 75°.

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

13. B. alt. ∠s, AB // CD
∠AEF and ∠EFD are alternate (a Z) and AB // CD, so they are equal: the reason is alt. ∠s, AB // CD.
14. 94°
Both are on one side, between the edges: interior angles. The edges are parallel, so they add to 180°: 180° − 86° = 94°.
15. A → C → B
Alternate angles are equal, ∠EFD = 135°; ∠EFC and ∠EFD lie on the line CD, so ∠EFC = 180° − 135° = 45°.
16. 42, 104
Moving terms: 3x − 2x = 20 + 22, x = 42. ∠AEF = 3 × 42 − 22 = 104°; the other, 2 × 42 + 20, is 104 too.
17. 60, 60
∠BEF = 180° − 120° = 60°. ∠BEF and ∠EFC are alternate and AB // CD, so ∠EFC = 60°.
18. 50°
See where x is from 50°: corresponding or alternate angles are equal; interior ones add to 180°. With parallel bars, every angle is 50° or 180° minus it.

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