Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 925 · 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 straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 165° (b) 16° (c) 15° (d) 195°
2. 2.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 20° (b) 30° (c) 40° (d) 140°
3. 3.Two angles of a triangle are 35° and 75°. What is the third angle? (a) 105° (b) 110° (c) 70° (d) 145°
4. 4.Two angles of a triangle are 40° and 100°. What is the third angle? (a) 220° (b) 40° (c) 140° (d) 80°
5. 5.Two angles of a triangle are 20° and 65°. What is the exterior angle at the third corner? (a) 160° (b) 95° (c) 85° (d) 115°
6. 6.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 60° (c) 120° (d) 30°
7. 7.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 30° (b) 150° (c) 95° (d) 115°
8. 8.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 40° (c) 70° (d) 110°
9. 9.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 100° (c) 80° (d) 40°
10. 10.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 145° (b) 55° (c) 160° (d) 125°
11. 11.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 265° (c) 85° (d) 95°
12. 12.Two angles of a triangle are 30° and 90°. What is the exterior angle at the third corner? (a) 60° (b) 150° (c) 90° (d) 120°
13. 13.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°
14. 14.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 50° (c) 40° (d) 70°
15. 15.Two angles of a triangle are 50° and 115°. What is the third angle? (a) 15° (b) 165° (c) 65° (d) 130°
16. 16.Two angles of a triangle are 65° and 100°. What is the third angle? (a) 115° (b) 15° (c) 165° (d) 80°
17. 17.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 130° (c) 65° (d) 155°
18. 18.Two angles of a triangle are 25° and 30°. What is the exterior angle at the third corner? (a) 155° (b) 125° (c) 55° (d) 150°
19. 19.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 60° (b) 240° (c) 121° (d) 120°
20. 20.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 10° (b) 80° (c) 280° (d) 100°
21. 21.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 270° (b) 150° (c) 120° (d) 90°
22. 22.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 120° (b) 140° (c) 100° (d) 60°
23. 23.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 85° (b) 190° (c) 95° (d) 10°
24. 24.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 310° (b) 50° (c) 130° (d) 40°
25. 25.Two angles of a triangle are 25° and 120°. What is the third angle? (a) 155° (b) 145° (c) 60° (d) 35°
26. 26.Two angles of a triangle are 45° and 50°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 130° (d) 135°
27. 27.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 70° (b) 290° (c) 110° (d) 145°
28. 28.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 30° (c) 60° (d) 120°
29. 29.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 35° (b) 145° (c) 115° (d) 100°
30. 30.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 20° (b) 320° (c) 160° (d) 140°
31. 31.Two angles of a triangle are 50° and 120°. What is the third angle? (a) 60° (b) 10° (c) 130° (d) 170°
32. 32.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 165° (b) 15° (c) 40° (d) 155°
33. 33.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) 125° (c) 55° (d) 56°
34. 34.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 105° (b) 135° (c) 75° (d) 120°
35. 35.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 155° (b) 335° (c) 25° (d) 65°
36. 36.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 100° (c) 105° (d) 80°
37. 37.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 35° (b) 145° (c) 70° (d) 36°
38. 38.Two angles of a triangle are 20° and 100°. What is the third angle? (a) 120° (b) 80° (c) 60° (d) 160°
39. 39.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 50° (c) 100° (d) 40°
40. 40.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 140° (b) 40° (c) 100° (d) 280°

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