Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 822 · 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. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 240° (b) 60° (c) 120° (d) 121°
2. 2.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 235° (b) 110° (c) 125° (d) 55°
3. 3.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 11° (b) 10° (c) 190° (d) 170°
4. 4.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 75° (b) 105° (c) 140° (d) 145°
5. 5.Two angles of a triangle are 45° and 60°. What is the exterior angle at the third corner? (a) 135° (b) 120° (c) 105° (d) 75°
6. 6.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 75° (b) 105° (c) 285° (d) 15°
7. 7.Two angles of a triangle are 30° and 80°. What is the exterior angle at the third corner? (a) 70° (b) 100° (c) 110° (d) 150°
8. 8.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 65° (c) 50° (d) 25°
9. 9.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 66° (b) 65° (c) 115° (d) 130°
10. 10.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 70° (b) 290° (c) 20° (d) 110°
11. 11.Two angles of a triangle are 30° and 70°. What is the third angle? (a) 80° (b) 110° (c) 150° (d) 100°
12. 12.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 145° (b) 290° (c) 110° (d) 35°
13. 13.Two angles of a triangle are 20° and 60°. What is the third angle? (a) 80° (b) 120° (c) 100° (d) 160°
14. 14.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 15° (b) 25° (c) 150° (d) 30°
15. 15.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 30° (b) 60° (c) 40° (d) 120°
16. 16.Two angles of a triangle are 70° and 75°. What is the third angle? (a) 35° (b) 110° (c) 145° (d) 105°
17. 17.Two angles of a triangle are 45° and 85°. What is the third angle? (a) 50° (b) 130° (c) 95° (d) 135°
18. 18.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 25° (c) 130° (d) 35°
19. 19.Two angles of a triangle are 35° and 85°. What is the third angle? (a) 120° (b) 145° (c) 95° (d) 60°
20. 20.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 70° (b) 340° (c) 160° (d) 20°
21. 21.Two angles of a triangle are 30° and 45°. What is the third angle? (a) 75° (b) 135° (c) 150° (d) 105°
22. 22.Two angles of a triangle are 80° and 90°. What is the third angle? (a) 100° (b) 170° (c) 90° (d) 10°
23. 23.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 80° (b) 130° (c) 50° (d) 260°
24. 24.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 70° (c) 60° (d) 30°
25. 25.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 100° (b) 280° (c) 140° (d) 40°
26. 26.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 30° (c) 40° (d) 20°
27. 27.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) 70° (c) 71° (d) 110°
28. 28.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 30° (c) 150° (d) 60°
29. 29.Two angles of a triangle are 25° and 115°. What is the third angle? (a) 155° (b) 65° (c) 140° (d) 40°
30. 30.Two angles of a triangle are 75° and 70°. What is the exterior angle at the third corner? (a) 145° (b) 105° (c) 110° (d) 35°
31. 31.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 30° (b) 100° (c) 150° (d) 110°
32. 32.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 100° (c) 80° (d) 50°
33. 33.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 10° (c) 20° (d) 11°
34. 34.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) 280° (c) 80° (d) 100°
35. 35.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 85° (c) 86° (d) 265°
36. 36.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 170° (b) 10° (c) 11° (d) 20°
37. 37.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) 110° (d) 40°
38. 38.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) 260° (c) 81° (d) 100°
39. 39.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 95° (b) 85° (c) 115° (d) 150°
40. 40.Two angles of a triangle are 70° and 65°. What is the third angle? (a) 135° (b) 115° (c) 45° (d) 110°

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