Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 917 · 40 questions

How to solve it (180 is the magic number): The three angles of a triangle add up to 180°. An exterior angle equals the sum of the two interior angles opposite it. An isosceles triangle has two equal angles, opposite its two equal sides. Angles on a straight line add up to 180°; vertically opposite angles are equal.

1. 1.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 310° (b) 130° (c) 25° (d) 155°
2. 2.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 70° (b) 145° (c) 290° (d) 110°
3. 3.Two angles of a triangle are 70° and 75°. What is the third angle? (a) 145° (b) 110° (c) 105° (d) 35°
4. 4.Two angles of a triangle are 50° and 105°. What is the third angle? (a) 130° (b) 75° (c) 155° (d) 25°
5. 5.Two angles of a triangle are 40° and 115°. What is the third angle? (a) 155° (b) 25° (c) 140° (d) 65°
6. 6.Two angles of a triangle are 75° and 30°. What is the third angle? (a) 255° (b) 150° (c) 75° (d) 105°
7. 7.Two angles of a triangle are 45° and 65°. What is the third angle? (a) 115° (b) 135° (c) 110° (d) 70°
8. 8.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 10° (b) 95° (c) 85° (d) 190°
9. 9.Two angles of a triangle are 30° and 85°. What is the exterior angle at the third corner? (a) 150° (b) 115° (c) 65° (d) 95°
10. 10.Two angles of a triangle are 70° and 70°. What is the third angle? (a) 110° (b) 220° (c) 40° (d) 140°
11. 11.Two angles of a triangle are 20° and 140°. What is the third angle? (a) 160° (b) 40° (c) 20° (d) 200°
12. 12.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 50° (b) 230° (c) 130° (d) 115°
13. 13.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 100° (b) 40° (c) 280° (d) 140°
14. 14.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 250° (b) 70° (c) 125° (d) 55°
15. 15.Two angles of a triangle are 20° and 80°. What is the exterior angle at the third corner? (a) 260° (b) 80° (c) 100° (d) 160°
16. 16.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 110° (b) 145° (c) 290° (d) 70°
17. 17.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 130° (b) 51° (c) 100° (d) 50°
18. 18.Two angles of a triangle are 70° and 45°. What is the exterior angle at the third corner? (a) 110° (b) 115° (c) 135° (d) 65°
19. 19.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 160° (b) 20° (c) 70° (d) 340°
20. 20.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 10° (c) 85° (d) 95°
21. 21.Two angles of a triangle are 55° and 75°. What is the third angle? (a) 130° (b) 50° (c) 125° (d) 105°
22. 22.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 45° (b) 155° (c) 135° (d) 70°
23. 23.Two angles of a triangle are 25° and 120°. What is the third angle? (a) 60° (b) 145° (c) 155° (d) 35°
24. 24.Two angles of a triangle are 25° and 85°. What is the third angle? (a) 95° (b) 70° (c) 110° (d) 155°
25. 25.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 40° (b) 130° (c) 50° (d) 310°
26. 26.Two angles of a triangle are 35° and 95°. What is the third angle? (a) 130° (b) 85° (c) 145° (d) 50°
27. 27.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 110° (b) 130° (c) 120° (d) 70°
28. 28.Two angles of a triangle are 40° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 140° (c) 145° (d) 35°
29. 29.Two angles of a triangle are 60° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 120° (c) 50° (d) 130°
30. 30.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 65° (b) 230° (c) 50° (d) 115°
31. 31.Two angles of a triangle are 20° and 35°. What is the exterior angle at the third corner? (a) 125° (b) 145° (c) 160° (d) 55°
32. 32.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 145° (c) 120° (d) 35°
33. 33.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 160° (b) 40° (c) 21° (d) 20°
34. 34.Two angles of a triangle are 65° and 40°. What is the exterior angle at the third corner? (a) 105° (b) 115° (c) 140° (d) 75°
35. 35.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 115° (b) 150° (c) 85° (d) 95°
36. 36.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 120° (b) 60° (c) 240° (d) 121°
37. 37.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 270° (b) 140° (c) 130° (d) 90°
38. 38.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 140° (c) 40° (d) 50°
39. 39.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 335° (b) 65° (c) 155° (d) 25°
40. 40.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 30° (b) 15° (c) 165° (d) 16°

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