Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 597 · 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 angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 130° (c) 40° (d) 50°
2. 2.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) 60° (c) 240° (d) 120°
3. 3.Two angles of a triangle are 35° and 90°. What is the exterior angle at the third corner? (a) 125° (b) 90° (c) 55° (d) 145°
4. 4.Two angles of a triangle are 20° and 65°. What is the third angle? (a) 95° (b) 85° (c) 160° (d) 115°
5. 5.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 250° (b) 140° (c) 110° (d) 70°
6. 6.Two angles of a triangle are 45° and 120°. What is the third angle? (a) 165° (b) 60° (c) 135° (d) 15°
7. 7.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 80° (b) 135° (c) 125° (d) 100°
8. 8.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 30° (b) 150° (c) 90° (d) 120°
9. 9.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 30° (b) 16° (c) 15° (d) 165°
10. 10.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 340° (b) 70° (c) 160° (d) 20°
11. 11.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°
12. 12.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 35° (b) 36° (c) 145° (d) 215°
13. 13.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 115° (c) 45° (d) 135°
14. 14.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 170° (b) 11° (c) 20° (d) 10°
15. 15.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 120° (b) 300° (c) 30° (d) 60°
16. 16.Two angles of a triangle are 30° and 110°. What is the third angle? (a) 70° (b) 40° (c) 140° (d) 150°
17. 17.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 11° (c) 160° (d) 10°
18. 18.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 30° (b) 31° (c) 210° (d) 150°
19. 19.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 55° (b) 56° (c) 125° (d) 110°
20. 20.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) 45° (d) 135°
21. 21.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 95° (c) 85° (d) 86°
22. 22.Two angles of a triangle are 25° and 120°. What is the third angle? (a) 35° (b) 60° (c) 155° (d) 145°
23. 23.Two angles of a triangle are 50° and 90°. What is the exterior angle at the third corner? (a) 40° (b) 140° (c) 90° (d) 130°
24. 24.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 95° (c) 86° (d) 85°
25. 25.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 255° (b) 76° (c) 75° (d) 105°
26. 26.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 55° (c) 70° (d) 35°
27. 27.Two angles of a triangle are 45° and 80°. What is the third angle? (a) 55° (b) 135° (c) 100° (d) 125°
28. 28.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 120° (c) 60° (d) 30°
29. 29.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 140° (c) 40° (d) 50°
30. 30.Two angles of a triangle are 65° and 45°. What is the exterior angle at the third corner? (a) 110° (b) 115° (c) 135° (d) 70°
31. 31.Two angles of a triangle are 60° and 25°. What is the exterior angle at the third corner? (a) 95° (b) 120° (c) 155° (d) 85°
32. 32.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 16° (b) 195° (c) 15° (d) 165°
33. 33.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 60° (c) 120° (d) 30°
34. 34.Two angles of a triangle are 75° and 60°. What is the third angle? (a) 120° (b) 135° (c) 45° (d) 105°
35. 35.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 110° (b) 60° (c) 120° (d) 130°
36. 36.Two angles of a triangle are 40° and 55°. What is the exterior angle at the third corner? (a) 85° (b) 140° (c) 125° (d) 95°
37. 37.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 150° (c) 30° (d) 120°
38. 38.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 40° (c) 80° (d) 130°
39. 39.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 40° (b) 20° (c) 21° (d) 160°
40. 40.Two angles of a triangle are 45° and 115°. What is the third angle? (a) 135° (b) 65° (c) 20° (d) 160°

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