Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 479 · 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 two equal angles are 75° each. What is the third angle? (a) 30° (b) 15° (c) 75° (d) 105°
2. 2.Two angles of a triangle are 45° and 95°. What is the third angle? (a) 40° (b) 135° (c) 85° (d) 140°
3. 3.Two angles of a triangle are 45° and 40°. What is the exterior angle at the third corner? (a) 95° (b) 140° (c) 135° (d) 85°
4. 4.Two angles of a triangle are 60° and 20°. What is the third angle? (a) 80° (b) 100° (c) 160° (d) 120°
5. 5.Two angles of a triangle are 20° and 55°. What is the exterior angle at the third corner? (a) 160° (b) 105° (c) 75° (d) 125°
6. 6.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 95° (c) 85° (d) 10°
7. 7.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 45° (c) 110° (d) 70°
8. 8.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 60° (b) 115° (c) 120° (d) 125°
9. 9.Two angles of a triangle are 55° and 70°. What is the exterior angle at the third corner? (a) 235° (b) 55° (c) 125° (d) 110°
10. 10.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 70° (c) 40° (d) 20°
11. 11.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 100° (c) 20° (d) 80°
12. 12.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) 295° (c) 115° (d) 65°
13. 13.Two angles of a triangle are 45° and 45°. What is the third angle? (a) 270° (b) 91° (c) 135° (d) 90°
14. 14.Two angles of a triangle are 70° and 20°. What is the third angle? (a) 270° (b) 90° (c) 160° (d) 110°
15. 15.Two angles of a triangle are 75° and 80°. What is the third angle? (a) 155° (b) 100° (c) 105° (d) 25°
16. 16.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 55° (b) 110° (c) 20° (d) 70°
17. 17.Two angles of a triangle are 55° and 30°. What is the exterior angle at the third corner? (a) 125° (b) 95° (c) 150° (d) 85°
18. 18.Two angles of a triangle are 30° and 20°. What is the exterior angle at the third corner? (a) 130° (b) 160° (c) 50° (d) 150°
19. 19.Two angles of a triangle are 30° and 125°. What is the third angle? (a) 155° (b) 55° (c) 25° (d) 150°
20. 20.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 91° (c) 45° (d) 90°
21. 21.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 235° (b) 56° (c) 125° (d) 55°
22. 22.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 75° (b) 145° (c) 105° (d) 110°
23. 23.Two angles of a triangle are 45° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 135° (c) 70° (d) 110°
24. 24.Two angles of a triangle are 25° and 55°. What is the third angle? (a) 80° (b) 155° (c) 125° (d) 100°
25. 25.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 40° (b) 140° (c) 105° (d) 115°
26. 26.Two angles of a triangle are 20° and 80°. What is the exterior angle at the third corner? (a) 160° (b) 100° (c) 260° (d) 80°
27. 27.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 150° (b) 270° (c) 90° (d) 120°
28. 28.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 260° (b) 130° (c) 50° (d) 80°
29. 29.Two angles of a triangle are 20° and 110°. What is the exterior angle at the third corner? (a) 50° (b) 130° (c) 70° (d) 160°
30. 30.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 130° (b) 155° (c) 25° (d) 310°
31. 31.Two angles of a triangle are 30° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 90° (c) 270° (d) 150°
32. 32.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 105° (b) 90° (c) 15° (d) 165°
33. 33.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 105° (c) 75° (d) 135°
34. 34.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 125° (c) 70° (d) 55°
35. 35.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 225° (b) 46° (c) 135° (d) 45°
36. 36.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 145° (b) 290° (c) 110° (d) 70°
37. 37.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 120° (b) 40° (c) 30° (d) 60°
38. 38.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 145° (c) 35° (d) 55°
39. 39.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 80° (b) 140° (c) 120° (d) 100°
40. 40.Two angles of a triangle are 30° and 75°. What is the exterior angle at the third corner? (a) 75° (b) 150° (c) 255° (d) 105°

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