Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 3 · 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 110°. What is the angle next to it on the same straight line? (a) 70° (b) 110° (c) 250° (d) 71°
2. 2.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 120° (b) 60° (c) 140° (d) 160°
3. 3.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 115° (b) 130° (c) 65° (d) 66°
4. 4.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 110° (d) 145°
5. 5.Two angles of a triangle are 25° and 45°. What is the third angle? (a) 70° (b) 135° (c) 155° (d) 110°
6. 6.Two angles of a triangle are 75° and 80°. What is the third angle? (a) 155° (b) 100° (c) 25° (d) 105°
7. 7.Two angles of a triangle are 40° and 75°. What is the third angle? (a) 105° (b) 65° (c) 115° (d) 140°
8. 8.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 40° (b) 110° (c) 220° (d) 70°
9. 9.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 95° (c) 170° (d) 86°
10. 10.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 55° (c) 46° (d) 45°
11. 11.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 80° (b) 81° (c) 160° (d) 100°
12. 12.Two angles of a triangle are 40° and 55°. What is the third angle? (a) 125° (b) 85° (c) 140° (d) 95°
13. 13.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 70° (b) 145° (c) 110° (d) 105°
14. 14.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) 125° (d) 250°
15. 15.Two angles of a triangle are 50° and 35°. What is the third angle? (a) 85° (b) 95° (c) 130° (d) 145°
16. 16.Two angles of a triangle are 35° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 95° (c) 145° (d) 85°
17. 17.Two angles of a triangle are 60° and 80°. What is the third angle? (a) 100° (b) 120° (c) 140° (d) 40°
18. 18.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 65° (c) 50° (d) 40°
19. 19.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°
20. 20.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 70° (c) 110° (d) 40°
21. 21.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 70° (b) 120° (c) 130° (d) 110°
22. 22.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°
23. 23.Two angles of a triangle are 40° and 35°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 140° (d) 145°
24. 24.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 61° (b) 240° (c) 60° (d) 120°
25. 25.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 10° (b) 85° (c) 5° (d) 95°
26. 26.Two angles of a triangle are 45° and 20°. What is the third angle? (a) 115° (b) 65° (c) 135° (d) 160°
27. 27.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 115° (b) 90° (c) 155° (d) 270°
28. 28.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 60° (b) 40° (c) 30° (d) 120°
29. 29.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 120° (c) 30° (d) 60°
30. 30.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 59° (b) 60° (c) 120° (d) 61°
31. 31.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°
32. 32.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°
33. 33.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 55° (b) 235° (c) 56° (d) 125°
34. 34.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 260° (b) 160° (c) 80° (d) 100°
35. 35.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 160° (c) 11° (d) 10°
36. 36.Two angles of a triangle are 35° and 60°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 145° (d) 120°
37. 37.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 145° (b) 35° (c) 290° (d) 110°
38. 38.Two angles of a triangle are 30° and 95°. What is the third angle? (a) 85° (b) 125° (c) 150° (d) 55°
39. 39.Two angles of a triangle are 75° and 85°. What is the third angle? (a) 160° (b) 20° (c) 105° (d) 95°
40. 40.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 320° (b) 50° (c) 140° (d) 40°

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