Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 98 · 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. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 120° (b) 30° (c) 300° (d) 60°
2. 2.Two angles of a triangle are 20° and 115°. What is the exterior angle at the third corner? (a) 65° (b) 160° (c) 45° (d) 135°
3. 3.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 150° (b) 90° (c) 120° (d) 270°
4. 4.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 81° (b) 100° (c) 80° (d) 160°
5. 5.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 110° (d) 145°
6. 6.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 160° (c) 10° (d) 11°
7. 7.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 155° (b) 85° (c) 120° (d) 95°
8. 8.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) 60° (d) 150°
9. 9.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 210° (b) 31° (c) 150° (d) 30°
10. 10.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 70° (b) 55° (c) 20° (d) 110°
11. 11.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 170° (b) 105° (c) 85° (d) 10°
12. 12.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 20° (c) 160° (d) 80°
13. 13.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 160° (d) 105°
14. 14.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 35° (c) 70° (d) 110°
15. 15.Two angles of a triangle are 40° and 30°. What is the exterior angle at the third corner? (a) 140° (b) 110° (c) 150° (d) 70°
16. 16.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 300° (b) 30° (c) 120° (d) 150°
17. 17.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 80° (b) 150° (c) 100° (d) 130°
18. 18.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 150° (b) 30° (c) 210° (d) 105°
19. 19.Two angles of a triangle are 30° and 75°. What is the exterior angle at the third corner? (a) 255° (b) 75° (c) 105° (d) 150°
20. 20.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 20° (c) 70° (d) 40°
21. 21.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 25° (c) 65° (d) 130°
22. 22.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 35° (b) 305° (c) 55° (d) 125°
23. 23.Two angles of a triangle are 20° and 130°. What is the third angle? (a) 160° (b) 50° (c) 30° (d) 150°
24. 24.Two angles of a triangle are 20° and 105°. What is the third angle? (a) 160° (b) 125° (c) 55° (d) 75°
25. 25.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 55° (c) 35° (d) 70°
26. 26.Two angles of a triangle are 25° and 65°. What is the exterior angle at the third corner? (a) 270° (b) 155° (c) 115° (d) 90°
27. 27.Two angles of a triangle are 60° and 20°. What is the third angle? (a) 120° (b) 100° (c) 80° (d) 160°
28. 28.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 115° (b) 105° (c) 40° (d) 140°
29. 29.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 25° (b) 130° (c) 35° (d) 50°
30. 30.Two angles of a triangle are 20° and 120°. What is the third angle? (a) 160° (b) 140° (c) 40° (d) 60°
31. 31.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 25° (c) 115° (d) 50°
32. 32.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 160° (c) 120° (d) 60°
33. 33.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 110° (b) 105° (c) 75° (d) 145°
34. 34.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) 40° (c) 41° (d) 220°
35. 35.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 50° (c) 100° (d) 140°
36. 36.Two angles of a triangle are 65° and 40°. What is the third angle? (a) 115° (b) 140° (c) 75° (d) 105°
37. 37.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 130° (c) 50° (d) 65°
38. 38.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 80° (c) 50° (d) 130°
39. 39.Two angles of a triangle are 20° and 45°. What is the exterior angle at the third corner? (a) 160° (b) 135° (c) 115° (d) 65°
40. 40.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 40° (c) 50° (d) 70°

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