Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 75 · 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 85° each. What is the third angle? (a) 95° (b) 5° (c) 10° (d) 85°
2. 2.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 300° (b) 60° (c) 120° (d) 30°
3. 3.Two angles of a triangle are 25° and 20°. What is the third angle? (a) 45° (b) 160° (c) 155° (d) 135°
4. 4.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 70° (b) 110° (c) 290° (d) 145°
5. 5.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 65° (b) 230° (c) 50° (d) 115°
6. 6.Two angles of a triangle are 70° and 65°. What is the third angle? (a) 115° (b) 45° (c) 135° (d) 110°
7. 7.Two angles of a triangle are 60° and 85°. What is the third angle? (a) 95° (b) 120° (c) 145° (d) 35°
8. 8.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 145° (b) 325° (c) 55° (d) 35°
9. 9.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 65° (b) 145° (c) 100° (d) 115°
10. 10.Two angles of a triangle are 40° and 95°. What is the exterior angle at the third corner? (a) 45° (b) 140° (c) 135° (d) 85°
11. 11.Two angles of a triangle are 20° and 115°. What is the third angle? (a) 65° (b) 135° (c) 45° (d) 160°
12. 12.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 130° (c) 25° (d) 155°
13. 13.Two angles of a triangle are 20° and 125°. What is the exterior angle at the third corner? (a) 35° (b) 145° (c) 160° (d) 55°
14. 14.Two angles of a triangle are 80° and 70°. What is the third angle? (a) 110° (b) 30° (c) 100° (d) 150°
15. 15.Two angles of a triangle are 25° and 110°. What is the third angle? (a) 70° (b) 155° (c) 135° (d) 45°
16. 16.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 75° (b) 30° (c) 210° (d) 105°
17. 17.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 140° (b) 110° (c) 71° (d) 70°
18. 18.Two angles of a triangle are 40° and 25°. What is the third angle? (a) 115° (b) 140° (c) 65° (d) 155°
19. 19.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 20° (b) 11° (c) 10° (d) 170°
20. 20.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 55° (c) 145° (d) 110°
21. 21.Two angles of a triangle are 35° and 90°. What is the third angle? (a) 145° (b) 90° (c) 55° (d) 125°
22. 22.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 25° (c) 50° (d) 115°
23. 23.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 15° (c) 30° (d) 75°
24. 24.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 60° (b) 140° (c) 160° (d) 120°
25. 25.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 295° (b) 115° (c) 65° (d) 25°
26. 26.Two angles of a triangle are 50° and 50°. What is the exterior angle at the third corner? (a) 260° (b) 100° (c) 80° (d) 130°
27. 27.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 310° (b) 130° (c) 40° (d) 50°
28. 28.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 30° (c) 60° (d) 70°
29. 29.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 280° (b) 80° (c) 10° (d) 100°
30. 30.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 70° (b) 40° (c) 110° (d) 220°
31. 31.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 110° (c) 150° (d) 80°
32. 32.Two angles of a triangle are 80° and 90°. What is the third angle? (a) 90° (b) 170° (c) 10° (d) 100°
33. 33.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 160° (b) 140° (c) 60° (d) 120°
34. 34.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 160° (b) 140° (c) 20° (d) 320°
35. 35.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 60° (b) 155° (c) 145° (d) 120°
36. 36.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 155° (c) 75° (d) 130°
37. 37.Two angles of a triangle are 60° and 60°. What is the third angle? (a) 60° (b) 120° (c) 240° (d) 61°
38. 38.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 120° (b) 240° (c) 121° (d) 60°
39. 39.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 150° (c) 60° (d) 120°
40. 40.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 50° (c) 80° (d) 10°

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