Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 162 · 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 20°. What is the angle next to it on the same straight line? (a) 20° (b) 340° (c) 70° (d) 160°
2. 2.Two angles of a triangle are 60° and 50°. What is the third angle? (a) 110° (b) 120° (c) 70° (d) 130°
3. 3.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 115° (b) 295° (c) 65° (d) 25°
4. 4.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 60° (c) 120° (d) 30°
5. 5.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 100° (b) 75° (c) 155° (d) 105°
6. 6.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 65° (b) 145° (c) 115° (d) 100°
7. 7.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 35° (c) 50° (d) 25°
8. 8.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 130° (c) 50° (d) 40°
9. 9.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 70° (c) 35° (d) 110°
10. 10.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 91° (c) 90° (d) 135°
11. 11.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 125° (b) 55° (c) 150° (d) 155°
12. 12.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 100° (b) 260° (c) 81° (d) 80°
13. 13.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 35° (b) 100° (c) 145° (d) 115°
14. 14.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) 85° (c) 95° (d) 265°
15. 15.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 75° (b) 105° (c) 255° (d) 76°
16. 16.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 30° (c) 60° (d) 120°
17. 17.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 130° (b) 65° (c) 115° (d) 66°
18. 18.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 45° (b) 90° (c) 46° (d) 135°
19. 19.Two angles of a triangle are 45° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 35° (c) 145° (d) 135°
20. 20.Two angles of a triangle are 25° and 110°. What is the third angle? (a) 155° (b) 135° (c) 45° (d) 70°
21. 21.Two angles of a triangle are 45° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 135° (c) 80° (d) 100°
22. 22.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 140° (b) 115° (c) 105° (d) 40°
23. 23.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 290° (b) 70° (c) 145° (d) 110°
24. 24.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 140° (b) 71° (c) 110° (d) 70°
25. 25.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 110° (c) 70° (d) 20°
26. 26.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°
27. 27.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°
28. 28.Two angles of a triangle are 55° and 25°. What is the exterior angle at the third corner? (a) 125° (b) 155° (c) 80° (d) 100°
29. 29.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 320° (b) 140° (c) 160° (d) 20°
30. 30.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 35° (b) 145° (c) 70° (d) 36°
31. 31.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) 120° (d) 61°
32. 32.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 105° (c) 75° (d) 30°
33. 33.Two angles of a triangle are 25° and 125°. What is the exterior angle at the third corner? (a) 55° (b) 150° (c) 30° (d) 155°
34. 34.Two angles of a triangle are 50° and 95°. What is the exterior angle at the third corner? (a) 35° (b) 145° (c) 85° (d) 130°
35. 35.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 140° (c) 50° (d) 70°
36. 36.Two angles of a triangle are 45° and 40°. What is the third angle? (a) 140° (b) 95° (c) 135° (d) 85°
37. 37.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 160° (d) 125°
38. 38.Two angles of a triangle are 65° and 95°. What is the third angle? (a) 160° (b) 85° (c) 115° (d) 20°
39. 39.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 25° (c) 155° (d) 65°
40. 40.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 120° (b) 300° (c) 150° (d) 30°

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