Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 20 · 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 30° each. What is the third angle? (a) 150° (b) 120° (c) 30° (d) 60°
2. 2.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 59° (b) 120° (c) 61° (d) 60°
3. 3.Two angles of a triangle are 30° and 65°. What is the exterior angle at the third corner? (a) 150° (b) 95° (c) 115° (d) 85°
4. 4.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 35° (d) 95°
5. 5.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 270° (c) 115° (d) 90°
6. 6.Two angles of a triangle are 30° and 120°. What is the third angle? (a) 30° (b) 210° (c) 60° (d) 150°
7. 7.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 60° (c) 30° (d) 61°
8. 8.Two angles of a triangle are 45° and 100°. What is the exterior angle at the third corner? (a) 135° (b) 35° (c) 145° (d) 80°
9. 9.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 120° (b) 140° (c) 100° (d) 80°
10. 10.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 70° (c) 110° (d) 45°
11. 11.Two angles of a triangle are 20° and 150°. What is the third angle? (a) 10° (b) 160° (c) 30° (d) 170°
12. 12.Two angles of a triangle are 45° and 60°. What is the exterior angle at the third corner? (a) 105° (b) 120° (c) 135° (d) 75°
13. 13.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 150° (c) 75° (d) 30°
14. 14.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 105° (d) 160°
15. 15.Two angles of a triangle are 65° and 50°. What is the third angle? (a) 115° (b) 130° (c) 245° (d) 65°
16. 16.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 55° (b) 235° (c) 125° (d) 56°
17. 17.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 30° (c) 25° (d) 15°
18. 18.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 125° (b) 55° (c) 70° (d) 250°
19. 19.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 75° (c) 30° (d) 15°
20. 20.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 100° (c) 65° (d) 115°
21. 21.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) 160° (c) 20° (d) 70°
22. 22.Two angles of a triangle are 60° and 80°. What is the third angle? (a) 140° (b) 100° (c) 40° (d) 120°
23. 23.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 95° (c) 86° (d) 85°
24. 24.Two angles of a triangle are 70° and 75°. What is the third angle? (a) 145° (b) 110° (c) 105° (d) 35°
25. 25.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 35° (c) 145° (d) 110°
26. 26.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 110° (b) 130° (c) 160° (d) 70°
27. 27.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 300° (b) 60° (c) 30° (d) 120°
28. 28.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 20° (c) 70° (d) 55°
29. 29.Two angles of a triangle are 45° and 20°. What is the exterior angle at the third corner? (a) 65° (b) 135° (c) 160° (d) 115°
30. 30.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 80° (b) 50° (c) 260° (d) 130°
31. 31.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 315° (b) 45° (c) 136° (d) 135°
32. 32.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 21° (b) 160° (c) 20° (d) 40°
33. 33.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 145° (b) 115° (c) 35° (d) 100°
34. 34.Two angles of a triangle are 40° and 35°. What is the exterior angle at the third corner? (a) 140° (b) 105° (c) 75° (d) 145°
35. 35.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 155° (c) 60° (d) 120°
36. 36.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 40° (c) 110° (d) 70°
37. 37.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 95° (c) 86° (d) 85°
38. 38.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 145° (c) 55° (d) 125°
39. 39.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 120° (b) 30° (c) 60° (d) 40°
40. 40.Two angles of a triangle are 25° and 65°. What is the third angle? (a) 155° (b) 90° (c) 115° (d) 270°

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