Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 460 · 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.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 120° (b) 40° (c) 60° (d) 30°
2. 2.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 155° (b) 25° (c) 310° (d) 130°
3. 3.Two angles of a triangle are 40° and 70°. What is the third angle? (a) 140° (b) 250° (c) 110° (d) 70°
4. 4.Two angles of a triangle are 30° and 115°. What is the exterior angle at the third corner? (a) 150° (b) 35° (c) 145° (d) 65°
5. 5.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 31° (b) 30° (c) 150° (d) 60°
6. 6.Two angles of a triangle are 25° and 30°. What is the exterior angle at the third corner? (a) 155° (b) 150° (c) 55° (d) 125°
7. 7.Two angles of a triangle are 55° and 85°. What is the exterior angle at the third corner? (a) 125° (b) 40° (c) 95° (d) 140°
8. 8.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 130° (c) 155° (d) 25°
9. 9.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 270° (b) 110° (c) 90° (d) 160°
10. 10.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 320° (b) 140° (c) 50° (d) 40°
11. 11.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) 50° (d) 100°
12. 12.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 45° (b) 46° (c) 225° (d) 135°
13. 13.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 85° (c) 86° (d) 95°
14. 14.Two angles of a triangle are 65° and 60°. What is the exterior angle at the third corner? (a) 125° (b) 55° (c) 115° (d) 120°
15. 15.Two angles of a triangle are 30° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 125° (c) 150° (d) 55°
16. 16.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 60° (b) 30° (c) 120° (d) 70°
17. 17.Two angles of a triangle are 60° and 95°. What is the third angle? (a) 85° (b) 25° (c) 120° (d) 155°
18. 18.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 140° (b) 320° (c) 20° (d) 160°
19. 19.Two angles of a triangle are 30° and 120°. What is the third angle? (a) 30° (b) 150° (c) 210° (d) 60°
20. 20.Two angles of a triangle are 45° and 100°. What is the exterior angle at the third corner? (a) 135° (b) 145° (c) 80° (d) 35°
21. 21.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 15° (c) 150° (d) 25°
22. 22.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 90° (c) 45° (d) 55°
23. 23.Two angles of a triangle are 20° and 80°. What is the exterior angle at the third corner? (a) 260° (b) 160° (c) 100° (d) 80°
24. 24.Two angles of a triangle are 80° and 45°. What is the third angle? (a) 135° (b) 55° (c) 100° (d) 125°
25. 25.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 125° (b) 250° (c) 70° (d) 55°
26. 26.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 105° (b) 145° (c) 70° (d) 110°
27. 27.Two angles of a triangle are 70° and 75°. What is the exterior angle at the third corner? (a) 145° (b) 35° (c) 105° (d) 110°
28. 28.Two angles of a triangle are 30° and 50°. What is the third angle? (a) 100° (b) 80° (c) 130° (d) 150°
29. 29.Two angles of a triangle are 25° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 95° (c) 155° (d) 85°
30. 30.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 230° (b) 50° (c) 115° (d) 65°
31. 31.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 25° (c) 35° (d) 130°
32. 32.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 140° (b) 41° (c) 40° (d) 220°
33. 33.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 60° (c) 75° (d) 30°
34. 34.Two angles of a triangle are 65° and 45°. What is the exterior angle at the third corner? (a) 115° (b) 110° (c) 135° (d) 70°
35. 35.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 75° (b) 210° (c) 30° (d) 105°
36. 36.Two angles of a triangle are 50° and 120°. What is the third angle? (a) 170° (b) 60° (c) 10° (d) 130°
37. 37.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 325° (b) 145° (c) 35° (d) 55°
38. 38.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 135° (b) 125° (c) 45° (d) 100°
39. 39.Two angles of a triangle are 55° and 55°. What is the exterior angle at the third corner? (a) 70° (b) 250° (c) 125° (d) 110°
40. 40.Two angles of a triangle are 80° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 100° (c) 50° (d) 230°

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