Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 64 · 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 angles of a triangle are 30° and 140°. What is the third angle? (a) 10° (b) 170° (c) 150° (d) 40°
2. 2.Two angles of a triangle are 40° and 65°. What is the third angle? (a) 105° (b) 75° (c) 140° (d) 115°
3. 3.Two angles of a triangle are 35° and 85°. What is the third angle? (a) 95° (b) 145° (c) 120° (d) 60°
4. 4.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 130° (b) 80° (c) 50° (d) 260°
5. 5.Two angles of a triangle are 25° and 60°. What is the third angle? (a) 155° (b) 120° (c) 85° (d) 95°
6. 6.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 50° (c) 230° (d) 130°
7. 7.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) 60° (d) 30°
8. 8.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 190° (b) 95° (c) 85° (d) 10°
9. 9.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 110° (b) 71° (c) 250° (d) 70°
10. 10.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 125° (c) 55° (d) 105°
11. 11.Two angles of a triangle are 30° and 30°. What is the exterior angle at the third corner? (a) 300° (b) 150° (c) 120° (d) 60°
12. 12.Two angles of a triangle are 45° and 25°. What is the third angle? (a) 155° (b) 70° (c) 135° (d) 110°
13. 13.Two angles of a triangle are 30° and 85°. What is the third angle? (a) 150° (b) 65° (c) 95° (d) 115°
14. 14.Two angles of a triangle are 70° and 80°. What is the third angle? (a) 100° (b) 150° (c) 110° (d) 30°
15. 15.Two angles of a triangle are 30° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 150° (c) 120° (d) 60°
16. 16.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 15° (c) 105° (d) 30°
17. 17.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 250° (b) 55° (c) 70° (d) 125°
18. 18.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 110° (c) 145° (d) 35°
19. 19.Two angles of a triangle are 20° and 75°. What is the third angle? (a) 105° (b) 85° (c) 95° (d) 160°
20. 20.Two angles of a triangle are 25° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 100° (c) 155° (d) 80°
21. 21.Two angles of a triangle are 25° and 20°. What is the third angle? (a) 45° (b) 160° (c) 155° (d) 135°
22. 22.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 61° (b) 120° (c) 59° (d) 60°
23. 23.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°
24. 24.Two angles of a triangle are 45° and 70°. What is the exterior angle at the third corner? (a) 65° (b) 110° (c) 135° (d) 115°
25. 25.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 60° (c) 150° (d) 30°
26. 26.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 20° (b) 21° (c) 200° (d) 160°
27. 27.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 315° (b) 136° (c) 135° (d) 45°
28. 28.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 245° (b) 65° (c) 115° (d) 66°
29. 29.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 70° (b) 115° (c) 110° (d) 135°
30. 30.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 145° (b) 155° (c) 120° (d) 60°
31. 31.Two angles of a triangle are 75° and 60°. What is the exterior angle at the third corner? (a) 45° (b) 120° (c) 105° (d) 135°
32. 32.Two angles of a triangle are 50° and 55°. What is the exterior angle at the third corner? (a) 130° (b) 75° (c) 125° (d) 105°
33. 33.Two angles of a triangle are 30° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 150° (c) 90° (d) 270°
34. 34.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 50° (c) 130° (d) 65°
35. 35.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 285° (b) 75° (c) 15° (d) 105°
36. 36.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°
37. 37.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 95° (b) 135° (c) 85° (d) 140°
38. 38.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) 35° (d) 130°
39. 39.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 100° (c) 10° (d) 50°
40. 40.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 130° (c) 80° (d) 50°

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