Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 307 · 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 35° and 120°. What is the third angle? (a) 145° (b) 155° (c) 60° (d) 25°
2. 2.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 120° (c) 150° (d) 30°
3. 3.Two angles of a triangle are 45° and 55°. What is the third angle? (a) 100° (b) 135° (c) 80° (d) 125°
4. 4.Two angles of a triangle are 35° and 85°. What is the third angle? (a) 60° (b) 95° (c) 120° (d) 145°
5. 5.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 25° (b) 130° (c) 155° (d) 310°
6. 6.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 145° (d) 105°
7. 7.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 20° (b) 80° (c) 10° (d) 100°
8. 8.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 155° (b) 105° (c) 80° (d) 100°
9. 9.Two angles of a triangle are 20° and 65°. What is the third angle? (a) 95° (b) 160° (c) 115° (d) 85°
10. 10.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 120° (c) 60° (d) 30°
11. 11.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 30° (b) 300° (c) 120° (d) 150°
12. 12.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 50° (c) 140° (d) 40°
13. 13.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 86° (c) 85° (d) 170°
14. 14.Two angles of a triangle are 80° and 85°. What is the third angle? (a) 15° (b) 165° (c) 100° (d) 95°
15. 15.Two angles of a triangle are 60° and 30°. What is the exterior angle at the third corner? (a) 270° (b) 120° (c) 150° (d) 90°
16. 16.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 130° (c) 40° (d) 65°
17. 17.Two angles of a triangle are 65° and 90°. What is the third angle? (a) 115° (b) 90° (c) 155° (d) 25°
18. 18.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 95° (b) 85° (c) 155° (d) 120°
19. 19.Two angles of a triangle are 20° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 95° (c) 160° (d) 85°
20. 20.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) 95° (c) 85° (d) 265°
21. 21.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 20° (c) 70° (d) 110°
22. 22.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 60° (b) 300° (c) 120° (d) 30°
23. 23.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 55° (c) 70° (d) 110°
24. 24.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 40° (c) 20° (d) 30°
25. 25.Two angles of a triangle are 60° and 45°. What is the exterior angle at the third corner? (a) 75° (b) 120° (c) 105° (d) 135°
26. 26.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 150° (b) 65° (c) 35° (d) 145°
27. 27.Two angles of a triangle are 55° and 90°. What is the third angle? (a) 90° (b) 35° (c) 145° (d) 125°
28. 28.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 51° (b) 230° (c) 130° (d) 50°
29. 29.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 280° (b) 100° (c) 140° (d) 40°
30. 30.Two angles of a triangle are 20° and 145°. What is the third angle? (a) 15° (b) 160° (c) 165° (d) 35°
31. 31.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 195° (b) 15° (c) 165° (d) 16°
32. 32.Two angles of a triangle are 65° and 30°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 115° (d) 150°
33. 33.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 130° (b) 110° (c) 50° (d) 120°
34. 34.Two angles of a triangle are 75° and 45°. What is the third angle? (a) 135° (b) 60° (c) 105° (d) 120°
35. 35.Two angles of a triangle are 20° and 75°. What is the third angle? (a) 105° (b) 160° (c) 85° (d) 95°
36. 36.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 110° (b) 70° (c) 20° (d) 290°
37. 37.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 130° (c) 155° (d) 65°
38. 38.Two angles of a triangle are 55° and 40°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 140° (d) 125°
39. 39.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 35° (c) 130° (d) 25°
40. 40.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) 40° (c) 130° (d) 50°

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