Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 768 · 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) 120° (b) 30° (c) 70° (d) 60°
2. 2.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 165° (b) 15° (c) 155° (d) 40°
3. 3.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) 30° (d) 210°
4. 4.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 80° (c) 40° (d) 130°
5. 5.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 30° (b) 120° (c) 40° (d) 60°
6. 6.Two angles of a triangle are 75° and 45°. What is the exterior angle at the third corner? (a) 105° (b) 120° (c) 135° (d) 60°
7. 7.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 95° (b) 150° (c) 85° (d) 115°
8. 8.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 100° (c) 50° (d) 40°
9. 9.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 155° (c) 25° (d) 65°
10. 10.Two angles of a triangle are 25° and 125°. What is the third angle? (a) 30° (b) 55° (c) 150° (d) 155°
11. 11.Two angles of a triangle are 20° and 115°. What is the third angle? (a) 160° (b) 65° (c) 45° (d) 135°
12. 12.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) 11° (d) 170°
13. 13.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°
14. 14.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 130° (c) 25° (d) 50°
15. 15.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 65° (c) 50° (d) 40°
16. 16.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 10° (b) 5° (c) 95° (d) 85°
17. 17.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 50° (b) 110° (c) 120° (d) 130°
18. 18.Two angles of a triangle are 50° and 100°. What is the third angle? (a) 30° (b) 80° (c) 130° (d) 150°
19. 19.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 60° (c) 120° (d) 150°
20. 20.Two angles of a triangle are 55° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 125° (c) 140° (d) 40°
21. 21.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 50° (b) 40° (c) 140° (d) 320°
22. 22.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 150° (b) 76° (c) 105° (d) 75°
23. 23.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 95° (b) 110° (c) 155° (d) 85°
24. 24.Two angles of a triangle are 45° and 55°. What is the third angle? (a) 80° (b) 135° (c) 125° (d) 100°
25. 25.Two angles of a triangle are 25° and 95°. What is the exterior angle at the third corner? (a) 120° (b) 155° (c) 60° (d) 85°
26. 26.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 120° (b) 60° (c) 240° (d) 121°
27. 27.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 150° (c) 60° (d) 75°
28. 28.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 70° (b) 155° (c) 135° (d) 45°
29. 29.Two angles of a triangle are 30° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 70° (c) 110° (d) 150°
30. 30.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 100° (c) 80° (d) 120°
31. 31.Two angles of a triangle are 50° and 75°. What is the third angle? (a) 125° (b) 105° (c) 130° (d) 55°
32. 32.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 125° (b) 70° (c) 250° (d) 55°
33. 33.Two angles of a triangle are 65° and 60°. What is the third angle? (a) 125° (b) 120° (c) 55° (d) 115°
34. 34.Two angles of a triangle are 45° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 45° (c) 135° (d) 225°
35. 35.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 55° (c) 46° (d) 45°
36. 36.Two angles of a triangle are 25° and 110°. What is the third angle? (a) 70° (b) 135° (c) 45° (d) 155°
37. 37.Two angles of a triangle are 30° and 110°. What is the third angle? (a) 140° (b) 70° (c) 40° (d) 150°
38. 38.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 95° (b) 10° (c) 85° (d) 190°
39. 39.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 20° (b) 160° (c) 21° (d) 200°
40. 40.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 130° (d) 155°

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