Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 317 · 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 angles of a triangle are 20° and 120°. What is the exterior angle at the third corner? (a) 160° (b) 60° (c) 40° (d) 140°
2. 2.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 150° (b) 31° (c) 210° (d) 30°
3. 3.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 145° (b) 110° (c) 290° (d) 35°
4. 4.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 75° (c) 150° (d) 60°
5. 5.Two angles of a triangle are 80° and 45°. What is the exterior angle at the third corner? (a) 55° (b) 135° (c) 100° (d) 125°
6. 6.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 66° (b) 115° (c) 65° (d) 130°
7. 7.Two angles of a triangle are 50° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 135° (c) 45° (d) 130°
8. 8.Two angles of a triangle are 30° and 20°. What is the third angle? (a) 150° (b) 160° (c) 130° (d) 50°
9. 9.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 45° (b) 46° (c) 90° (d) 135°
10. 10.Two angles of a triangle are 25° and 25°. What is the third angle? (a) 50° (b) 310° (c) 155° (d) 130°
11. 11.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 20° (b) 10° (c) 170° (d) 11°
12. 12.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 120° (b) 35° (c) 95° (d) 145°
13. 13.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 270° (b) 90° (c) 45° (d) 135°
14. 14.Two angles of a triangle are 40° and 50°. What is the third angle? (a) 270° (b) 140° (c) 90° (d) 130°
15. 15.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 120° (b) 160° (c) 60° (d) 140°
16. 16.Two angles of a triangle are 65° and 60°. What is the third angle? (a) 120° (b) 125° (c) 115° (d) 55°
17. 17.Two angles of a triangle are 75° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 45° (c) 135° (d) 105°
18. 18.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 85° (c) 95° (d) 265°
19. 19.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 50° (b) 130° (c) 40° (d) 310°
20. 20.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 150° (b) 130° (c) 80° (d) 100°
21. 21.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 255° (b) 76° (c) 105° (d) 75°
22. 22.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 155° (b) 100° (c) 80° (d) 105°
23. 23.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 45° (b) 315° (c) 136° (d) 135°
24. 24.Two angles of a triangle are 45° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 135° (c) 105° (d) 75°
25. 25.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 75° (b) 150° (c) 135° (d) 105°
26. 26.Two angles of a triangle are 20° and 45°. What is the third angle? (a) 65° (b) 115° (c) 160° (d) 135°
27. 27.Two angles of a triangle are 40° and 60°. What is the exterior angle at the third corner? (a) 100° (b) 120° (c) 80° (d) 140°
28. 28.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 100° (d) 125°
29. 29.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 20° (b) 110° (c) 290° (d) 70°
30. 30.Two angles of a triangle are 70° and 70°. What is the exterior angle at the third corner? (a) 40° (b) 220° (c) 140° (d) 110°
31. 31.Two angles of a triangle are 70° and 70°. What is the third angle? (a) 140° (b) 110° (c) 40° (d) 220°
32. 32.Two angles of a triangle are 40° and 55°. What is the third angle? (a) 95° (b) 85° (c) 140° (d) 125°
33. 33.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 55° (b) 35° (c) 325° (d) 145°
34. 34.Two angles of a triangle are 55° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 125° (c) 120° (d) 60°
35. 35.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 120° (b) 61° (c) 60° (d) 240°
36. 36.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 55° (b) 70° (c) 110° (d) 20°
37. 37.Two angles of a triangle are 45° and 55°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 125° (d) 135°
38. 38.Two angles of a triangle are 30° and 80°. What is the third angle? (a) 110° (b) 150° (c) 70° (d) 100°
39. 39.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 120° (b) 115° (c) 55° (d) 125°
40. 40.Two angles of a triangle are 75° and 55°. What is the third angle? (a) 50° (b) 125° (c) 105° (d) 130°

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