Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 338 · 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 angles of a triangle are 60° and 25°. What is the exterior angle at the third corner? (a) 120° (b) 155° (c) 85° (d) 95°
2. 2.Two angles of a triangle are 60° and 50°. What is the exterior angle at the third corner? (a) 110° (b) 130° (c) 120° (d) 70°
3. 3.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 60° (c) 70° (d) 30°
4. 4.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 250° (b) 110° (c) 70° (d) 71°
5. 5.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 15° (b) 165° (c) 30° (d) 16°
6. 6.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 135° (b) 100° (c) 80° (d) 125°
7. 7.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 110° (b) 145° (c) 290° (d) 35°
8. 8.Two angles of a triangle are 40° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 140° (c) 100° (d) 80°
9. 9.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 50° (c) 80° (d) 40°
10. 10.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 85° (c) 86° (d) 95°
11. 11.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 50° (c) 25° (d) 35°
12. 12.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) 55° (c) 145° (d) 35°
13. 13.Two angles of a triangle are 50° and 115°. What is the third angle? (a) 130° (b) 15° (c) 165° (d) 65°
14. 14.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 160° (b) 40° (c) 21° (d) 20°
15. 15.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 130° (c) 25° (d) 65°
16. 16.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 100° (b) 80° (c) 81° (d) 160°
17. 17.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) 200° (c) 21° (d) 160°
18. 18.Two angles of a triangle are 25° and 70°. What is the third angle? (a) 155° (b) 95° (c) 85° (d) 110°
19. 19.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 105° (b) 130° (c) 125° (d) 55°
20. 20.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 40° (b) 70° (c) 220° (d) 110°
21. 21.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 50° (c) 80° (d) 100°
22. 22.Two angles of a triangle are 70° and 65°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 110° (d) 115°
23. 23.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 70° (c) 125° (d) 55°
24. 24.Two angles of a triangle are 20° and 110°. What is the third angle? (a) 130° (b) 70° (c) 50° (d) 160°
25. 25.Two angles of a triangle are 20° and 95°. What is the exterior angle at the third corner? (a) 160° (b) 65° (c) 85° (d) 115°
26. 26.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 90° (b) 135° (c) 45° (d) 46°
27. 27.Two angles of a triangle are 30° and 65°. What is the third angle? (a) 95° (b) 115° (c) 85° (d) 150°
28. 28.Two angles of a triangle are 35° and 105°. What is the third angle? (a) 140° (b) 40° (c) 145° (d) 75°
29. 29.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 61° (b) 120° (c) 60° (d) 240°
30. 30.Two angles of a triangle are 35° and 60°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 95° (d) 85°
31. 31.Two angles of a triangle are 25° and 105°. What is the exterior angle at the third corner? (a) 155° (b) 75° (c) 130° (d) 50°
32. 32.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 290° (b) 145° (c) 110° (d) 70°
33. 33.Two angles of a triangle are 30° and 110°. What is the exterior angle at the third corner? (a) 40° (b) 70° (c) 140° (d) 150°
34. 34.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 105° (b) 55° (c) 125° (d) 130°
35. 35.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 140° (c) 40° (d) 70°
36. 36.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 100° (b) 80° (c) 260° (d) 81°
37. 37.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 20° (c) 40° (d) 70°
38. 38.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 190° (b) 10° (c) 11° (d) 170°
39. 39.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 40° (b) 140° (c) 80° (d) 41°
40. 40.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 50° (c) 40° (d) 65°

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