Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 77 · 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 55°. What is the angle next to it on the same straight line? (a) 55° (b) 35° (c) 125° (d) 305°
2. 2.Two angles of a triangle are 65° and 35°. What is the third angle? (a) 80° (b) 100° (c) 145° (d) 115°
3. 3.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 65° (b) 66° (c) 115° (d) 130°
4. 4.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 250° (b) 71° (c) 70° (d) 110°
5. 5.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 60° (b) 330° (c) 150° (d) 30°
6. 6.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 75° (b) 150° (c) 255° (d) 105°
7. 7.Two angles of a triangle are 25° and 85°. What is the third angle? (a) 110° (b) 95° (c) 155° (d) 70°
8. 8.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 160° (b) 21° (c) 40° (d) 20°
9. 9.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 190° (b) 10° (c) 95° (d) 85°
10. 10.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 25° (c) 130° (d) 65°
11. 11.Two angles of a triangle are 35° and 110°. What is the exterior angle at the third corner? (a) 215° (b) 35° (c) 70° (d) 145°
12. 12.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 70° (c) 125° (d) 35°
13. 13.Two angles of a triangle are 25° and 50°. What is the third angle? (a) 130° (b) 105° (c) 155° (d) 75°
14. 14.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 41° (b) 40° (c) 140° (d) 80°
15. 15.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 30° (b) 105° (c) 75° (d) 210°
16. 16.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 136° (b) 315° (c) 45° (d) 135°
17. 17.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 105° (b) 75° (c) 76° (d) 255°
18. 18.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 150° (c) 30° (d) 60°
19. 19.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 260° (b) 80° (c) 130° (d) 50°
20. 20.Two angles of a triangle are 30° and 140°. What is the third angle? (a) 10° (b) 150° (c) 170° (d) 40°
21. 21.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°
22. 22.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 145° (b) 35° (c) 110° (d) 105°
23. 23.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 290° (b) 110° (c) 70° (d) 145°
24. 24.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 140° (c) 40° (d) 50°
25. 25.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) 190° (c) 10° (d) 11°
26. 26.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 40° (b) 140° (c) 220° (d) 41°
27. 27.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 260° (b) 80° (c) 81° (d) 100°
28. 28.Two angles of a triangle are 20° and 90°. What is the third angle? (a) 90° (b) 160° (c) 70° (d) 110°
29. 29.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 105° (b) 285° (c) 75° (d) 15°
30. 30.Two angles of a triangle are 60° and 105°. What is the third angle? (a) 165° (b) 120° (c) 75° (d) 15°
31. 31.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 105° (d) 130°
32. 32.Two angles of a triangle are 30° and 45°. What is the exterior angle at the third corner? (a) 150° (b) 105° (c) 135° (d) 75°
33. 33.Two angles of a triangle are 60° and 65°. What is the third angle? (a) 125° (b) 115° (c) 55° (d) 120°
34. 34.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 100° (b) 145° (c) 35° (d) 115°
35. 35.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 70° (c) 80° (d) 160°
36. 36.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 120° (c) 61° (d) 30°
37. 37.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 85° (c) 10° (d) 5°
38. 38.Two angles of a triangle are 25° and 75°. What is the third angle? (a) 80° (b) 155° (c) 105° (d) 100°
39. 39.Two angles of a triangle are 30° and 60°. What is the third angle? (a) 270° (b) 90° (c) 120° (d) 150°
40. 40.Two angles of a triangle are 30° and 80°. What is the third angle? (a) 100° (b) 150° (c) 70° (d) 110°

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