Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 122 · 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 60°. What is each of the other two angles? (a) 60° (b) 30° (c) 120° (d) 70°
2. 2.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 60° (c) 120° (d) 100°
3. 3.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 95° (c) 5° (d) 10°
4. 4.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 140° (c) 40° (d) 100°
5. 5.Two angles of a triangle are 65° and 75°. What is the third angle? (a) 115° (b) 40° (c) 140° (d) 105°
6. 6.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 70° (b) 290° (c) 145° (d) 110°
7. 7.Two angles of a triangle are 40° and 30°. What is the third angle? (a) 150° (b) 110° (c) 140° (d) 70°
8. 8.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 100° (b) 35° (c) 115° (d) 145°
9. 9.Two angles of a triangle are 45° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 135° (c) 130° (d) 50°
10. 10.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 20° (c) 40° (d) 140°
11. 11.Two angles of a triangle are 75° and 65°. What is the exterior angle at the third corner? (a) 140° (b) 105° (c) 40° (d) 115°
12. 12.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 70° (b) 125° (c) 55° (d) 35°
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) 95° (c) 86° (d) 85°
14. 14.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 160° (b) 60° (c) 120° (d) 140°
15. 15.Two angles of a triangle are 20° and 65°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 160° (d) 115°
16. 16.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 150° (c) 15° (d) 25°
17. 17.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 150° (c) 120° (d) 60°
18. 18.Two angles of a triangle are 25° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 155° (c) 125° (d) 55°
19. 19.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 60° (b) 61° (c) 240° (d) 120°
20. 20.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 70° (c) 35° (d) 110°
21. 21.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 30° (c) 60° (d) 120°
22. 22.Two angles of a triangle are 50° and 90°. What is the third angle? (a) 140° (b) 40° (c) 90° (d) 130°
23. 23.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 80° (c) 40° (d) 100°
24. 24.Two angles of a triangle are 40° and 95°. What is the exterior angle at the third corner? (a) 140° (b) 135° (c) 45° (d) 85°
25. 25.Two angles of a triangle are 30° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 85° (c) 150° (d) 95°
26. 26.Two angles of a triangle are 75° and 80°. What is the third angle? (a) 155° (b) 25° (c) 105° (d) 100°
27. 27.Two angles of a triangle are 55° and 80°. What is the exterior angle at the third corner? (a) 125° (b) 135° (c) 45° (d) 100°
28. 28.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 80° (b) 81° (c) 100° (d) 160°
29. 29.Two angles of a triangle are 50° and 20°. What is the third angle? (a) 160° (b) 130° (c) 70° (d) 110°
30. 30.Two angles of a triangle are 20° and 20°. What is the third angle? (a) 160° (b) 320° (c) 140° (d) 40°
31. 31.Two angles of a triangle are 25° and 120°. What is the exterior angle at the third corner? (a) 155° (b) 35° (c) 60° (d) 145°
32. 32.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 130° (b) 310° (c) 50° (d) 40°
33. 33.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 260° (b) 81° (c) 80° (d) 100°
34. 34.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 110° (b) 70° (c) 40° (d) 220°
35. 35.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 155° (b) 25° (c) 105° (d) 100°
36. 36.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 150° (b) 30° (c) 210° (d) 105°
37. 37.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 40° (c) 50° (d) 80°
38. 38.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 160° (c) 80° (d) 70°
39. 39.Two angles of a triangle are 60° and 100°. What is the third angle? (a) 80° (b) 120° (c) 160° (d) 20°
40. 40.Two angles of a triangle are 30° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 115° (c) 65° (d) 150°

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