Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 562 · 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 40°. What is each of the other two angles? (a) 70° (b) 40° (c) 50° (d) 140°
2. 2.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 125° (b) 145° (c) 160° (d) 55°
3. 3.Two angles of a triangle are 40° and 25°. What is the third angle? (a) 65° (b) 155° (c) 115° (d) 140°
4. 4.Two angles of a triangle are 40° and 125°. What is the third angle? (a) 165° (b) 140° (c) 55° (d) 15°
5. 5.Two angles of a triangle are 75° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 45° (c) 135° (d) 105°
6. 6.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 80° (b) 81° (c) 260° (d) 100°
7. 7.Two angles of a triangle are 30° and 40°. What is the exterior angle at the third corner? (a) 150° (b) 70° (c) 140° (d) 110°
8. 8.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 100° (b) 20° (c) 200° (d) 80°
9. 9.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 35° (b) 145° (c) 90° (d) 125°
10. 10.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 110° (b) 80° (c) 150° (d) 100°
11. 11.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 145° (b) 140° (c) 75° (d) 105°
12. 12.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 25° (b) 335° (c) 65° (d) 155°
13. 13.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 80° (b) 125° (c) 135° (d) 100°
14. 14.Two angles of a triangle are 40° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 140° (c) 270° (d) 90°
15. 15.Two angles of a triangle are 45° and 75°. What is the exterior angle at the third corner? (a) 135° (b) 60° (c) 105° (d) 120°
16. 16.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 35° (c) 70° (d) 55°
17. 17.Two angles of a triangle are 25° and 45°. What is the third angle? (a) 135° (b) 70° (c) 155° (d) 110°
18. 18.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 35° (c) 145° (d) 110°
19. 19.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 40° (c) 130° (d) 65°
20. 20.Two angles of a triangle are 20° and 70°. What is the third angle? (a) 110° (b) 270° (c) 160° (d) 90°
21. 21.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) 95° (d) 85°
22. 22.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 110° (b) 155° (c) 85° (d) 95°
23. 23.Two angles of a triangle are 20° and 90°. What is the third angle? (a) 110° (b) 90° (c) 160° (d) 70°
24. 24.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 170° (b) 11° (c) 10° (d) 190°
25. 25.Two angles of a triangle are 70° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 110° (c) 145° (d) 35°
26. 26.Two angles of a triangle are 45° and 110°. What is the third angle? (a) 25° (b) 70° (c) 155° (d) 135°
27. 27.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 65° (c) 155° (d) 130°
28. 28.Two angles of a triangle are 25° and 30°. What is the third angle? (a) 125° (b) 155° (c) 150° (d) 55°
29. 29.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 70° (b) 220° (c) 40° (d) 110°
30. 30.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 40° (b) 21° (c) 160° (d) 20°
31. 31.Two angles of a triangle are 30° and 90°. What is the third angle? (a) 120° (b) 60° (c) 90° (d) 150°
32. 32.Two angles of a triangle are 20° and 150°. What is the third angle? (a) 160° (b) 170° (c) 10° (d) 30°
33. 33.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) 110° (d) 290°
34. 34.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 60° (c) 30° (d) 120°
35. 35.Two angles of a triangle are 30° and 55°. What is the third angle? (a) 125° (b) 85° (c) 95° (d) 150°
36. 36.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 45° (c) 110° (d) 35°
37. 37.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 305° (b) 55° (c) 35° (d) 125°
38. 38.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 150° (c) 15° (d) 30°
39. 39.Two angles of a triangle are 30° and 65°. What is the third angle? (a) 95° (b) 85° (c) 115° (d) 150°
40. 40.Two angles of a triangle are 20° and 85°. What is the exterior angle at the third corner? (a) 75° (b) 95° (c) 105° (d) 160°

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