Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 83 · 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 160°. What is each of the other two angles? (a) 160° (b) 20° (c) 10° (d) 11°
2. 2.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 155° (b) 105° (c) 130° (d) 75°
3. 3.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 65° (c) 155° (d) 130°
4. 4.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 110° (b) 135° (c) 115° (d) 70°
5. 5.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 50° (b) 120° (c) 110° (d) 130°
6. 6.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 60° (b) 120° (c) 30° (d) 40°
7. 7.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 295° (b) 25° (c) 115° (d) 65°
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) 120° (c) 70° (d) 30°
9. 9.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) 120° (c) 30° (d) 60°
10. 10.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 20° (b) 150° (c) 50° (d) 160°
11. 11.Two angles of a triangle are 40° and 115°. What is the third angle? (a) 25° (b) 140° (c) 155° (d) 65°
12. 12.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 80° (c) 50° (d) 100°
13. 13.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) 115° (c) 66° (d) 65°
14. 14.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 155° (b) 85° (c) 95° (d) 120°
15. 15.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 11° (b) 190° (c) 170° (d) 10°
16. 16.Two angles of a triangle are 70° and 60°. What is the third angle? (a) 50° (b) 110° (c) 120° (d) 130°
17. 17.Two angles of a triangle are 60° and 25°. What is the exterior angle at the third corner? (a) 85° (b) 120° (c) 155° (d) 95°
18. 18.Two angles of a triangle are 25° and 60°. What is the exterior angle at the third corner? (a) 85° (b) 155° (c) 120° (d) 95°
19. 19.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 5° (c) 85° (d) 10°
20. 20.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 45° (b) 90° (c) 135° (d) 270°
21. 21.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) 30° (d) 75°
22. 22.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 145° (b) 125° (c) 90° (d) 270°
23. 23.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 300° (b) 30° (c) 150° (d) 120°
24. 24.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 70° (b) 71° (c) 140° (d) 110°
25. 25.Two angles of a triangle are 65° and 50°. What is the third angle? (a) 115° (b) 245° (c) 130° (d) 65°
26. 26.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 45° (b) 90° (c) 135° (d) 46°
27. 27.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 70° (c) 35° (d) 55°
28. 28.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 55° (b) 145° (c) 125° (d) 160°
29. 29.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 40° (c) 70° (d) 50°
30. 30.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 36° (b) 215° (c) 35° (d) 145°
31. 31.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 65° (b) 25° (c) 335° (d) 155°
32. 32.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 115° (b) 120° (c) 60° (d) 125°
33. 33.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 105° (b) 145° (c) 110° (d) 75°
34. 34.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 210° (b) 75° (c) 105° (d) 30°
35. 35.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 70° (b) 35° (c) 145° (d) 215°
36. 36.Two angles of a triangle are 50° and 45°. What is the exterior angle at the third corner? (a) 85° (b) 135° (c) 95° (d) 130°
37. 37.Two angles of a triangle are 60° and 30°. What is the exterior angle at the third corner? (a) 270° (b) 90° (c) 150° (d) 120°
38. 38.Two angles of a triangle are 35° and 80°. What is the third angle? (a) 100° (b) 145° (c) 115° (d) 65°
39. 39.Two angles of a triangle are 25° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 105° (c) 75° (d) 155°
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) 45° (c) 135° (d) 225°

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