Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 200 · 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 angles of a triangle are 25° and 40°. What is the third angle? (a) 65° (b) 140° (c) 115° (d) 155°
2. 2.Two angles of a triangle are 35° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 65° (c) 145° (d) 115°
3. 3.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 100° (b) 105° (c) 155° (d) 80°
4. 4.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 55° (b) 325° (c) 145° (d) 35°
5. 5.Two angles of a triangle are 35° and 105°. What is the exterior angle at the third corner? (a) 140° (b) 40° (c) 145° (d) 75°
6. 6.Two angles of a triangle are 45° and 55°. What is the third angle? (a) 100° (b) 125° (c) 80° (d) 135°
7. 7.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 51° (b) 100° (c) 130° (d) 50°
8. 8.Two angles of a triangle are 50° and 75°. What is the exterior angle at the third corner? (a) 125° (b) 130° (c) 55° (d) 105°
9. 9.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 31° (b) 210° (c) 30° (d) 150°
10. 10.Two angles of a triangle are 45° and 85°. What is the third angle? (a) 135° (b) 95° (c) 130° (d) 50°
11. 11.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) 35° (c) 145° (d) 215°
12. 12.Two angles of a triangle are 80° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 100° (c) 125° (d) 55°
13. 13.Two angles of a triangle are 25° and 105°. What is the exterior angle at the third corner? (a) 155° (b) 50° (c) 130° (d) 75°
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) 70° (d) 40°
15. 15.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 145° (b) 140° (c) 75° (d) 105°
16. 16.Two angles of a triangle are 70° and 80°. What is the third angle? (a) 110° (b) 30° (c) 150° (d) 100°
17. 17.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 60° (c) 61° (d) 120°
18. 18.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 10° (b) 11° (c) 160° (d) 20°
19. 19.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 145° (c) 55° (d) 35°
20. 20.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 150° (c) 75° (d) 60°
21. 21.Two angles of a triangle are 50° and 90°. What is the third angle? (a) 140° (b) 130° (c) 40° (d) 90°
22. 22.Two angles of a triangle are 25° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 70° (c) 110° (d) 155°
23. 23.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 60° (b) 240° (c) 61° (d) 120°
24. 24.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 125° (b) 56° (c) 55° (d) 110°
25. 25.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 35° (b) 290° (c) 145° (d) 110°
26. 26.Two angles of a triangle are 70° and 75°. What is the third angle? (a) 35° (b) 145° (c) 110° (d) 105°
27. 27.Two angles of a triangle are 35° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 85° (c) 145° (d) 95°
28. 28.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 125° (c) 70° (d) 35°
29. 29.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 46° (c) 90° (d) 45°
30. 30.Two angles of a triangle are 45° and 105°. What is the third angle? (a) 135° (b) 150° (c) 75° (d) 30°
31. 31.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 81° (b) 100° (c) 160° (d) 80°
32. 32.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 260° (b) 50° (c) 130° (d) 80°
33. 33.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 170° (c) 85° (d) 86°
34. 34.Two angles of a triangle are 25° and 65°. What is the exterior angle at the third corner? (a) 90° (b) 270° (c) 155° (d) 115°
35. 35.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 130° (c) 40° (d) 65°
36. 36.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 120° (b) 70° (c) 130° (d) 110°
37. 37.Two angles of a triangle are 60° and 85°. What is the third angle? (a) 120° (b) 35° (c) 95° (d) 145°
38. 38.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) 35° (d) 110°
39. 39.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 70° (c) 55° (d) 110°
40. 40.Two angles of a triangle are 75° and 65°. What is the exterior angle at the third corner? (a) 105° (b) 115° (c) 40° (d) 140°

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