Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 56 · 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 55° and 20°. What is the third angle? (a) 75° (b) 160° (c) 125° (d) 105°
2. 2.Two angles of a triangle are 45° and 45°. What is the exterior angle at the third corner? (a) 91° (b) 90° (c) 270° (d) 135°
3. 3.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) 160° (c) 200° (d) 21°
4. 4.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 160° (b) 20° (c) 70° (d) 340°
5. 5.Two angles of a triangle are 50° and 35°. What is the third angle? (a) 85° (b) 95° (c) 145° (d) 130°
6. 6.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 55° (c) 105° (d) 125°
7. 7.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 105° (b) 120° (c) 75° (d) 135°
8. 8.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 140° (b) 160° (c) 120° (d) 60°
9. 9.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 15° (c) 150° (d) 30°
10. 10.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 70° (b) 145° (c) 110° (d) 290°
11. 11.Two angles of a triangle are 45° and 80°. What is the exterior angle at the third corner? (a) 125° (b) 135° (c) 100° (d) 55°
12. 12.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 80° (c) 260° (d) 100°
13. 13.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 60° (b) 30° (c) 120° (d) 70°
14. 14.Two angles of a triangle are 25° and 125°. What is the exterior angle at the third corner? (a) 30° (b) 55° (c) 150° (d) 155°
15. 15.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 15° (b) 40° (c) 165° (d) 155°
16. 16.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 100° (b) 120° (c) 40° (d) 140°
17. 17.Two angles of a triangle are 80° and 45°. What is the exterior angle at the third corner? (a) 100° (b) 55° (c) 135° (d) 125°
18. 18.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 145° (b) 35° (c) 36° (d) 215°
19. 19.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 100° (c) 80° (d) 50°
20. 20.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 61° (c) 60° (d) 30°
21. 21.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 110° (d) 115°
22. 22.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 60° (b) 120° (c) 155° (d) 145°
23. 23.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 50° (c) 130° (d) 40°
24. 24.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 30° (b) 120° (c) 300° (d) 60°
25. 25.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 250° (b) 71° (c) 70° (d) 110°
26. 26.Two angles of a triangle are 30° and 100°. What is the third angle? (a) 150° (b) 80° (c) 130° (d) 50°
27. 27.Two angles of a triangle are 60° and 105°. What is the third angle? (a) 75° (b) 120° (c) 15° (d) 165°
28. 28.Two angles of a triangle are 60° and 70°. What is the exterior angle at the third corner? (a) 50° (b) 120° (c) 110° (d) 130°
29. 29.Two angles of a triangle are 35° and 60°. What is the third angle? (a) 120° (b) 145° (c) 95° (d) 85°
30. 30.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 140° (b) 41° (c) 40° (d) 80°
31. 31.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 20° (b) 160° (c) 140° (d) 320°
32. 32.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 155° (b) 50° (c) 25° (d) 26°
33. 33.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 265° (c) 85° (d) 86°
34. 34.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 310° (b) 130° (c) 155° (d) 25°
35. 35.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 130° (c) 25° (d) 35°
36. 36.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 10° (b) 5° (c) 95° (d) 85°
37. 37.Two angles of a triangle are 65° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 115° (c) 60° (d) 120°
38. 38.Two angles of a triangle are 55° and 90°. What is the third angle? (a) 145° (b) 35° (c) 90° (d) 125°
39. 39.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 90° (c) 45° (d) 55°
40. 40.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 115° (c) 140° (d) 40°

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