Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 469 · 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 40°. What is each of the other two angles? (a) 320° (b) 20° (c) 160° (d) 140°
2. 2.Two angles of a triangle are 55° and 70°. What is the exterior angle at the third corner? (a) 235° (b) 55° (c) 110° (d) 125°
3. 3.Two angles of a triangle are 45° and 90°. What is the third angle? (a) 225° (b) 90° (c) 135° (d) 45°
4. 4.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 85° (c) 95° (d) 170°
5. 5.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 60° (b) 30° (c) 330° (d) 150°
6. 6.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 71° (b) 110° (c) 140° (d) 70°
7. 7.Two angles of a triangle are 20° and 130°. What is the third angle? (a) 160° (b) 150° (c) 30° (d) 50°
8. 8.Two angles of a triangle are 20° and 45°. What is the third angle? (a) 135° (b) 115° (c) 65° (d) 160°
9. 9.Two angles of a triangle are 50° and 70°. What is the exterior angle at the third corner? (a) 60° (b) 130° (c) 110° (d) 120°
10. 10.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°
11. 11.Two angles of a triangle are 65° and 60°. What is the third angle? (a) 120° (b) 55° (c) 125° (d) 115°
12. 12.Two angles of a triangle are 40° and 95°. What is the third angle? (a) 85° (b) 140° (c) 45° (d) 135°
13. 13.Two angles of a triangle are 35° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 85° (c) 145° (d) 95°
14. 14.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 130° (c) 70° (d) 110°
15. 15.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 15° (b) 105° (c) 75° (d) 285°
16. 16.Two angles of a triangle are 80° and 20°. What is the third angle? (a) 260° (b) 80° (c) 160° (d) 100°
17. 17.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 145° (b) 60° (c) 120° (d) 155°
18. 18.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 55° (c) 70° (d) 20°
19. 19.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 310° (b) 25° (c) 130° (d) 155°
20. 20.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 160° (c) 70° (d) 340°
21. 21.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 95° (b) 150° (c) 85° (d) 115°
22. 22.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°
23. 23.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 60° (b) 145° (c) 120° (d) 155°
24. 24.Two angles of a triangle are 30° and 40°. What is the third angle? (a) 150° (b) 140° (c) 70° (d) 110°
25. 25.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 90° (c) 46° (d) 45°
26. 26.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 155° (b) 130° (c) 75° (d) 105°
27. 27.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°
28. 28.Two angles of a triangle are 60° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 120° (c) 115° (d) 65°
29. 29.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 30° (c) 60° (d) 75°
30. 30.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 130° (c) 40° (d) 50°
31. 31.Two angles of a triangle are 30° and 75°. What is the exterior angle at the third corner? (a) 255° (b) 150° (c) 75° (d) 105°
32. 32.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 80° (b) 130° (c) 260° (d) 50°
33. 33.Two angles of a triangle are 25° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 155° (c) 115° (d) 65°
34. 34.Two angles of a triangle are 60° and 60°. What is the third angle? (a) 120° (b) 240° (c) 60° (d) 61°
35. 35.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 140° (b) 320° (c) 40° (d) 50°
36. 36.Two angles of a triangle are 30° and 65°. What is the third angle? (a) 95° (b) 150° (c) 115° (d) 85°
37. 37.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 55° (c) 110° (d) 145°
38. 38.Two angles of a triangle are 70° and 65°. What is the third angle? (a) 135° (b) 45° (c) 115° (d) 110°
39. 39.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 120° (b) 300° (c) 150° (d) 30°
40. 40.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 100° (c) 80° (d) 50°

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