Geometry and proof · Ages 12–13
Bends and reflex angles worksheet
Part of: Angles & parallel lines
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Bends and reflex angles worksheet
Geometry and proof · Ages 12–13
Numsprite
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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.
Part A: Working out and filling in (2 marks each)
1.The two lines are parallel. x =
Answer:
2.The two lines are parallel, and the angle at the bend is marked. x =
Answer:
3.The two lines are parallel, as shown. x =
Answer:
4.The two lines are parallel. The reflex angle x outside the bend =
Answer:
5.The two lines are parallel. 180° − 140° = °, 180° − 136° = °, x = °.
Fill in each blank
Answer:
6.The two lines are parallel. 180° − 150° = °, 180° − 125° = °, x = °.
Fill in each blank
Answer:
7.The two lines are parallel. The reflex angle x outside the bend =
Answer:
8.The two lines are parallel, and the reflex angle outside the bend is 278°. x =
Answer:
9.The two lines are parallel, and the reflex angle outside the bend is 300°. x =
Answer:
Part B: Choose, or true or false (2 marks each)
10.The two lines are parallel, and the dashed line through the bend is parallel to them. What is x?
- A. 109°
- B. 71°
- C. 251°
- D. 25°
Choose the right answer
Answer:
11.The two lines are parallel. The reflex angle x outside the bend = 282°.
True or false?
Answer:
12.The two lines are parallel. The reflex angle x outside the bend = 242°.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.The two lines are parallel, as shown. What is x?
- A. 83°
- B. 97°
- C. 113°
- D. 277°
Choose the right answer
Working:
Answer:
14.The two lines are parallel and the path turns a right angle at the bend, as shown. What is x?
Working:
Answer:
15.An iron rod runs from the upper rail, bends at a point and reaches the lower rail; the rails are parallel, as shown. x is the reflex angle on the outside of the bend. What is x?
Working:
Answer:
16.A pipe runs down from the ceiling, bends at a point, and runs on down to the floor; ceiling and floor are parallel, as shown. What is the angle x at the bend?
Working:
Answer:
17.The two lines are parallel, as shown: a = (x + 9)°, b = 2x° and c = (4x − 11)°. The angle at the bend equals the two beside it added: (x + 9) + 2x = 4x − 11, x = , c = °.
Fill in each blank
Working:
Answer:
18.The two lines are parallel; the dashed line through the bend is parallel to them. The upper part of x = 48° (______). Which reason goes in the blank?
- A. alt. ∠s
- B. vert. opp. ∠s
- C. int. ∠s
- D. corr. ∠s
Choose the right answer
Working:
Answer:
Show the answers and working
Bends and reflex angles worksheet: Answers and working
Part A: Working out and filling in
1. 76°
Draw a line through the bend parallel to both: it splits x into two alternate angles, x = 38° + 38° = 76° (alt. ∠s).
2. 57°
A parallel line through the bend splits its angle into two alternate angles: 108° = 51° + x, x = 108° − 51° = 57° (alt. ∠s).
3. 111°
Where the picture gives the angle beside one, take it from 180° first (adj. ∠s on st. line): 38° and 73°. A parallel line through the bend: x = 38° + 73° = 111° (alt. ∠s).
4. 251°
The smaller angle at the bend = 68° + 41° = 109° (alt. ∠s); x = 360° − 109° = 251° (∠s at a pt.).
5. 40, 44, 84
Beside 140° is 180° − 140° = 40°, beside 136° is 180° − 136° = 44° (adj. ∠s on st. line); a parallel line through the bend: x = 40° + 44° = 84° (alt. ∠s).
6. 30, 55, 85
Beside 150° is 180° − 150° = 30°, beside 125° is 180° − 125° = 55° (adj. ∠s on st. line); a parallel line through the bend: x = 30° + 55° = 85° (alt. ∠s).
7. 282°
A marked angle on the far side of the bent line turns into the alternate one first (adj. ∠s on st. line): 43° at A and 35° at B. The smaller angle at the bend = 43° + 35° = 78° (alt. ∠s), and x = 360° − 78° = 282° (∠s at a pt.).
8. 43°
The smaller angle at the bend = 360° − 278° = 82° (∠s at a pt.); a parallel line through the bend: 82° = 39° + x, x = 82° − 39° = 43° (alt. ∠s).
9. 34°
The smaller angle at the bend = 360° − 300° = 60° (∠s at a pt.); a parallel line through the bend: 60° = 26° + x, x = 60° − 26° = 34° (alt. ∠s).
Part B: Choose, or true or false
10. A. 109°
The dashed line splits x in two: the upper part = 67°, the lower = 42° (alt. ∠s). x = 67° + 42° = 109°.
11. False
The smaller angle = 60° + 42° = 102° (alt. ∠s), x = 360° − 102° = 258° (∠s at a pt.).
12. False
The smaller angle = 36° + 26° = 62° (alt. ∠s), x = 360° − 62° = 298° (∠s at a pt.).
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. A. 83°
Next to 127° is 180° − 127° = 53°, next to 150° is 30° (adj. ∠s on st. line). A parallel line through the bend: x = 53° + 30° = 83°. Or 360° − 127° − 150° = 83°.
14. 35°
The bend's angle is the two alternate angles added: 55° + x = 90°, x = 90° − 55° = 35°.
15. 274°
The angle inside the bend = 36° + 50° = 86° (a parallel line through it, two alternate angles). The reflex angle = 360° − 86° = 274° (∠s at a pt.).
16. 54°
Draw a line through the bend parallel to the ceiling: it splits x into two alternate angles, x = 25° + 29° = 54°.
17. 20, 69
3x + 9 = 4x − 11; moving terms, x = 9 + 11 = 20. c = 4 × 20 − 11 = 69°; check: a + b = 29° + 40° = 69°.
18. A. alt. ∠s
The dashed line is parallel to the top line, and one piece of the path is a transversal: the upper part of x and 48° are alternate, so equal. x = 48° + 66° = 114°.
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