Geometry and proof · Ages 12–13
Angles & parallel lines worksheet
Covers: Angles on a line and at a point, Vertically opposite angles, Angles with an unknown, Corresponding, alternate and interior angles, Telling parallel lines, Angles with parallel lines, Bends and reflex angles, Angles of a triangle, Isosceles triangles
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Angles & parallel lines worksheet
Geometry and proof · Ages 12–13
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.The four angles go round one point. x =
Answer:
2.The four angles go round one point, and the two marked x are equal. x =
Answer:
3.Two straight lines cross, as shown. x =
Answer:
4.Three straight lines meet at a point, as shown. x =
Answer:
5.The two angles lie on a straight line. x =
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6.Two straight lines cross; the two angles written with x are vertically opposite. x =
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7.In the picture AB // CD. x =
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8.The two lines are parallel, as shown. x =
Answer:
9.One side of the triangle is extended, and the exterior angle is marked. x =
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10.In the picture AB = AC, ∠BAC = 58°, and BC is extended to D. ∠ACB = °, ∠ACD = °.
Fill in each blank
Answer:
Part B: Choose, or true or false (2 marks each)
11.In each picture two parallel lines are cut by a transversal, one angle 50°. In which are a and b alternate angles?
- A
- B
- C
- D
Choose the right picture
Answer:
12.The two marked angles are corresponding angles. The two lines are parallel.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.At 10 o'clock, what is the reflex angle (more than 180°) between the hour hand and the minute hand?
Working:
Answer:
14.Two straight roads cross in an X. One angle is 12° more than the angle next to it. What is the larger angle?
Working:
Answer:
15.AB // CD and ∠AEF = 105°, as shown. ∠EFD = ∠AEF = 105° (______). Which reason goes in the blank?
- A. int. ∠s, AB // CD
- B. vert. opp. ∠s
- C. alt. ∠s, AB // CD
- D. corr. ∠s, AB // CD
Choose the right answer
Working:
Answer:
16.The two lines are parallel. Through the bend draw a line parallel to them (dashed). The upper part of x = ° (alt. ∠s), the lower part = ° (alt. ∠s), so x = °.
Fill in each blank
Working:
Answer:
17.One side of the triangle is extended, as shown. What is x?
- A. 149°
- B. 72°
- C. 77°
- D. 134°
Choose the right answer
Working:
Answer:
18.One angle of an isosceles triangle is 38°. The other two can be 38° and °, or ° and °.
Fill in each blank
Working:
Answer:
Show the answers and working
Angles & parallel lines worksheet: Answers and working
Part A: Working out and filling in
1. 112°
x + 93° + 65° + 90° = 360° (∠s at a pt.), so x = 360° − 93° − 65° − 90° = 112°. The right angle counts too.
2. 86°
x + x + 127° + 61° = 360° (∠s at a pt.), 2x = 360° − 127° − 61° = 172°, x = 86°.
3. 35°
x and 145° sit side by side on one straight line: x = 180° − 145° = 35° (adj. ∠s on st. line).
4. 70°
The angle opposite 33° lies on one straight line with 77° and x: x = 180° − 33° − 77° = 70° (vert. opp. ∠s, adj. ∠s on st. line).
5. 15
(5x + 24) + 81 = 180 (adj. ∠s on st. line), 5x = 180 − 81 − 24 = 75, x = 15.
6. 18
Vertically opposite angles are equal: 4x + 28 = 7x − 26 (vert. opp. ∠s), 3x = 28 + 26 = 54, x = 18.
7. 19
The two are on opposite sides, both between AB and CD: alternate angles, so equal. 2x + 12 = 3x − 7 (alt. ∠s, AB // CD), x = 19, x = 19.
8. 96°
Where the picture gives the angle beside one, take it from 180° first (adj. ∠s on st. line): 40° and 56°. A parallel line through the bend: x = 40° + 56° = 96° (alt. ∠s).
9. 83°
The exterior angle 116° equals the two far interior angles added: x + 33° = 116° (ext. ∠ of △), so x = 116° − 33° = 83°.
10. 61, 119
∠ACB = (180° − 58°) ÷ 2 = 61° (base ∠s, isos. △), ∠ACD = 180° − 61° = 119° (adj. ∠s on st. line).
Part B: Choose, or true or false
11. D
Alternate angles are on opposite sides of the transversal and both between the lines, making a Z.
12. False
The lines are parallel only if corresponding angles are equal (corr. ∠s equal). Here they are 70° and 67°.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 300°
Each space is 30°, so the smaller angle is 60°. The two angles go round the centre and add to 360° (∠s at a pt.): the reflex angle = 360° − 60° = 300°.
14. 96°
Angles side by side add to 180° (adj. ∠s on st. line). With y the smaller: y + (y + 12) = 180, y = 84, so the larger is 96°.
15. C. 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.
16. 36, 35, 71
The dashed line is parallel to the top one, so x's upper part and 36° are alternate: 36°. The lower part and 35° are alternate too: 35°. x = 36° + 35° = 71°.
17. B. 72°
The exterior angle 103° is x and 31° added (ext. ∠ of △): x = 103° − 31° = 72°.
18. 104, 71, 71
Two cases: if 38° is a base angle, so is the other, and the top = 180° − 2 × 38° = 104°; if 38° is the top, each base angle = (180° − 38°) ÷ 2 = 71°.
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