Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 157 · 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 70° and 60°. What is the exterior angle at the third corner? (a) 130° (b) 110° (c) 50° (d) 120°
2. 2.Two angles of a triangle are 65° and 25°. What is the third angle? (a) 90° (b) 115° (c) 155° (d) 270°
3. 3.Two angles of a triangle are 50° and 120°. What is the third angle? (a) 60° (b) 130° (c) 170° (d) 10°
4. 4.Two angles of a triangle are 35° and 135°. What is the third angle? (a) 45° (b) 10° (c) 170° (d) 145°
5. 5.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 125° (c) 55° (d) 70°
6. 6.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 105° (b) 150° (c) 76° (d) 75°
7. 7.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 160° (b) 110° (c) 70° (d) 130°
8. 8.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 60° (b) 30° (c) 70° (d) 120°
9. 9.Two angles of a triangle are 45° and 40°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 135° (d) 140°
10. 10.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 50° (c) 25° (d) 115°
11. 11.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 145° (b) 105° (c) 110° (d) 35°
12. 12.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 170° (c) 85° (d) 95°
13. 13.Two angles of a triangle are 45° and 90°. What is the third angle? (a) 225° (b) 90° (c) 135° (d) 45°
14. 14.Two angles of a triangle are 55° and 95°. What is the third angle? (a) 85° (b) 30° (c) 125° (d) 150°
15. 15.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 25° (b) 115° (c) 295° (d) 65°
16. 16.Two angles of a triangle are 35° and 25°. What is the third angle? (a) 145° (b) 60° (c) 155° (d) 120°
17. 17.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 20° (b) 80° (c) 10° (d) 100°
18. 18.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 115° (b) 140° (c) 105° (d) 40°
19. 19.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) 40° (c) 50° (d) 320°
20. 20.Two angles of a triangle are 75° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 65° (c) 105° (d) 115°
21. 21.Two angles of a triangle are 50° and 105°. What is the third angle? (a) 155° (b) 25° (c) 130° (d) 75°
22. 22.Two angles of a triangle are 75° and 60°. What is the third angle? (a) 45° (b) 105° (c) 120° (d) 135°
23. 23.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) 170° (c) 10° (d) 11°
24. 24.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 105° (c) 155° (d) 75°
25. 25.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 11° (c) 160° (d) 10°
26. 26.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 30° (c) 60° (d) 150°
27. 27.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 145° (b) 35° (c) 290° (d) 110°
28. 28.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 31° (b) 150° (c) 30° (d) 60°
29. 29.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 136° (b) 315° (c) 45° (d) 135°
30. 30.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 30° (b) 75° (c) 105° (d) 15°
31. 31.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 45° (b) 155° (c) 135° (d) 70°
32. 32.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 140° (d) 145°
33. 33.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 80° (c) 50° (d) 130°
34. 34.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 105° (b) 75° (c) 76° (d) 255°
35. 35.Two angles of a triangle are 35° and 130°. What is the third angle? (a) 145° (b) 50° (c) 15° (d) 165°
36. 36.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 30° (c) 75° (d) 150°
37. 37.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 10° (c) 5° (d) 95°
38. 38.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 340° (b) 70° (c) 160° (d) 20°
39. 39.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 55° (b) 305° (c) 125° (d) 35°
40. 40.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 50° (b) 65° (c) 115° (d) 230°

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