Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 13 · 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 70°. What is each of the other two angles? (a) 55° (b) 70° (c) 110° (d) 20°
2. 2.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 110° (b) 250° (c) 70° (d) 140°
3. 3.Two angles of a triangle are 65° and 85°. What is the third angle? (a) 150° (b) 115° (c) 95° (d) 30°
4. 4.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 290° (b) 110° (c) 20° (d) 70°
5. 5.Two angles of a triangle are 45° and 95°. What is the third angle? (a) 135° (b) 40° (c) 85° (d) 140°
6. 6.Two angles of a triangle are 25° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 110° (c) 70° (d) 155°
7. 7.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 110° (c) 55° (d) 35°
8. 8.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 75° (b) 15° (c) 285° (d) 105°
9. 9.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 110° (b) 40° (c) 70° (d) 220°
10. 10.Two angles of a triangle are 20° and 60°. What is the third angle? (a) 100° (b) 160° (c) 120° (d) 80°
11. 11.Two angles of a triangle are 30° and 105°. What is the third angle? (a) 75° (b) 45° (c) 135° (d) 150°
12. 12.Two angles of a triangle are 45° and 70°. What is the third angle? (a) 115° (b) 135° (c) 110° (d) 65°
13. 13.Two angles of a triangle are 50° and 120°. What is the third angle? (a) 60° (b) 10° (c) 170° (d) 130°
14. 14.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 80° (b) 100° (c) 200° (d) 20°
15. 15.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 155° (c) 100° (d) 80°
16. 16.Two angles of a triangle are 55° and 55°. What is the third angle? (a) 110° (b) 250° (c) 70° (d) 125°
17. 17.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 75° (b) 255° (c) 76° (d) 105°
18. 18.Two angles of a triangle are 60° and 65°. What is the third angle? (a) 120° (b) 55° (c) 115° (d) 125°
19. 19.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 75° (b) 145° (c) 105° (d) 110°
20. 20.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 50° (c) 80° (d) 40°
21. 21.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 55° (c) 90° (d) 45°
22. 22.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 140° (b) 320° (c) 20° (d) 160°
23. 23.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 40° (b) 140° (c) 115° (d) 105°
24. 24.Two angles of a triangle are 20° and 115°. What is the third angle? (a) 135° (b) 160° (c) 45° (d) 65°
25. 25.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 155° (b) 26° (c) 25° (d) 205°
26. 26.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 60° (c) 30° (d) 61°
27. 27.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 86° (c) 85° (d) 265°
28. 28.Two angles of a triangle are 55° and 40°. What is the exterior angle at the third corner? (a) 85° (b) 140° (c) 95° (d) 125°
29. 29.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 65° (b) 115° (c) 230° (d) 50°
30. 30.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 26° (b) 155° (c) 25° (d) 50°
31. 31.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 70° (c) 120° (d) 60°
32. 32.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 125° (b) 160° (c) 145° (d) 55°
33. 33.Two angles of a triangle are 75° and 55°. What is the exterior angle at the third corner? (a) 50° (b) 125° (c) 105° (d) 130°
34. 34.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 81° (b) 160° (c) 80° (d) 100°
35. 35.Two angles of a triangle are 20° and 50°. What is the third angle? (a) 70° (b) 130° (c) 160° (d) 110°
36. 36.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 245° (b) 65° (c) 66° (d) 115°
37. 37.Two angles of a triangle are 45° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 135° (c) 115° (d) 65°
38. 38.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 100° (c) 80° (d) 10°
39. 39.Two angles of a triangle are 60° and 80°. What is the exterior angle at the third corner? (a) 120° (b) 100° (c) 40° (d) 140°
40. 40.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 46° (b) 135° (c) 45° (d) 225°

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