Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 137 · 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 two equal angles are 75° each. What is the third angle? (a) 30° (b) 75° (c) 15° (d) 105°
2. 2.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 135° (b) 45° (c) 315° (d) 136°
3. 3.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 125° (b) 110° (c) 235° (d) 55°
4. 4.Two angles of a triangle are 30° and 125°. What is the third angle? (a) 150° (b) 155° (c) 55° (d) 25°
5. 5.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) 35° (c) 325° (d) 145°
6. 6.Two angles of a triangle are 20° and 140°. What is the third angle? (a) 160° (b) 40° (c) 20° (d) 200°
7. 7.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 150° (b) 330° (c) 60° (d) 30°
8. 8.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 290° (b) 35° (c) 110° (d) 145°
9. 9.Two angles of a triangle are 25° and 100°. What is the exterior angle at the third corner? (a) 155° (b) 55° (c) 125° (d) 80°
10. 10.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 115° (b) 65° (c) 245° (d) 66°
11. 11.Two angles of a triangle are 75° and 45°. What is the third angle? (a) 135° (b) 60° (c) 120° (d) 105°
12. 12.Two angles of a triangle are 35° and 115°. What is the third angle? (a) 150° (b) 65° (c) 30° (d) 145°
13. 13.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 30° (b) 210° (c) 150° (d) 31°
14. 14.Two angles of a triangle are 65° and 90°. What is the third angle? (a) 115° (b) 25° (c) 90° (d) 155°
15. 15.Two angles of a triangle are 30° and 110°. What is the third angle? (a) 70° (b) 140° (c) 40° (d) 150°
16. 16.Two angles of a triangle are 55° and 115°. What is the third angle? (a) 170° (b) 125° (c) 10° (d) 65°
17. 17.Two angles of a triangle are 45° and 35°. What is the third angle? (a) 145° (b) 80° (c) 100° (d) 135°
18. 18.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 280° (b) 140° (c) 40° (d) 100°
19. 19.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 85° (b) 115° (c) 95° (d) 150°
20. 20.Two angles of a triangle are 55° and 20°. What is the third angle? (a) 75° (b) 105° (c) 125° (d) 160°
21. 21.Two angles of a triangle are 50° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 85° (c) 130° (d) 95°
22. 22.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 105° (b) 55° (c) 125° (d) 130°
23. 23.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 155° (b) 25° (c) 100° (d) 105°
24. 24.Two angles of a triangle are 25° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 100° (c) 155° (d) 80°
25. 25.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 31° (b) 30° (c) 150° (d) 60°
26. 26.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 160° (b) 81° (c) 100° (d) 80°
27. 27.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 35° (c) 110° (d) 45°
28. 28.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 120° (c) 61° (d) 30°
29. 29.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 110° (b) 100° (c) 150° (d) 70°
30. 30.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 130° (d) 155°
31. 31.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 55° (b) 70° (c) 250° (d) 125°
32. 32.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) 65° (c) 25° (d) 335°
33. 33.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 45° (c) 90° (d) 135°
34. 34.Two angles of a triangle are 20° and 135°. What is the third angle? (a) 45° (b) 25° (c) 160° (d) 155°
35. 35.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) 120° (c) 61° (d) 240°
36. 36.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 270° (b) 90° (c) 45° (d) 135°
37. 37.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 145° (b) 75° (c) 105° (d) 140°
38. 38.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 45° (b) 95° (c) 135° (d) 130°
39. 39.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 260° (c) 80° (d) 130°
40. 40.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 130° (b) 310° (c) 25° (d) 155°

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