Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 266 · 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 110°. What is each of the other two angles? (a) 45° (b) 35° (c) 110° (d) 70°
2. 2.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 75° (b) 76° (c) 150° (d) 105°
3. 3.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 70° (c) 35° (d) 55°
4. 4.Two angles of a triangle are 60° and 105°. What is the third angle? (a) 75° (b) 165° (c) 15° (d) 120°
5. 5.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 70° (b) 140° (c) 110° (d) 71°
6. 6.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°
7. 7.Two angles of a triangle are 30° and 100°. What is the exterior angle at the third corner? (a) 150° (b) 130° (c) 50° (d) 80°
8. 8.Two angles of a triangle are 25° and 95°. What is the exterior angle at the third corner? (a) 60° (b) 155° (c) 120° (d) 85°
9. 9.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) 300° (c) 120° (d) 60°
10. 10.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 70° (b) 55° (c) 125° (d) 250°
11. 11.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) 15° (c) 105° (d) 75°
12. 12.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 105° (b) 145° (c) 75° (d) 140°
13. 13.Two angles of a triangle are 70° and 60°. What is the third angle? (a) 110° (b) 120° (c) 130° (d) 50°
14. 14.Two angles of a triangle are 45° and 80°. What is the third angle? (a) 125° (b) 135° (c) 55° (d) 100°
15. 15.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 45° (c) 91° (d) 90°
16. 16.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) 215° (c) 36° (d) 35°
17. 17.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 270° (b) 145° (c) 90° (d) 125°
18. 18.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 50° (c) 70° (d) 40°
19. 19.Two angles of a triangle are 30° and 110°. What is the third angle? (a) 150° (b) 40° (c) 140° (d) 70°
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) 135° (c) 136° (d) 45°
21. 21.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 280° (c) 140° (d) 100°
22. 22.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 85° (c) 10° (d) 95°
23. 23.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°
24. 24.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 155° (b) 65° (c) 335° (d) 25°
25. 25.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 135° (b) 45° (c) 270° (d) 90°
26. 26.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°
27. 27.Two angles of a triangle are 75° and 55°. What is the exterior angle at the third corner? (a) 130° (b) 105° (c) 50° (d) 125°
28. 28.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 150° (c) 65° (d) 115°
29. 29.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 80° (c) 260° (d) 130°
30. 30.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 70° (c) 40° (d) 110°
31. 31.Two angles of a triangle are 75° and 45°. What is the third angle? (a) 135° (b) 105° (c) 60° (d) 120°
32. 32.Two angles of a triangle are 20° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 160° (c) 95° (d) 85°
33. 33.Two angles of a triangle are 25° and 60°. What is the exterior angle at the third corner? (a) 95° (b) 155° (c) 85° (d) 120°
34. 34.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 60° (b) 120° (c) 61° (d) 240°
35. 35.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 70° (b) 20° (c) 55° (d) 110°
36. 36.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 85° (c) 95° (d) 86°
37. 37.Two angles of a triangle are 55° and 40°. What is the exterior angle at the third corner? (a) 125° (b) 85° (c) 140° (d) 95°
38. 38.Two angles of a triangle are 55° and 85°. What is the exterior angle at the third corner? (a) 140° (b) 95° (c) 125° (d) 40°
39. 39.Two angles of a triangle are 35° and 115°. What is the exterior angle at the third corner? (a) 65° (b) 150° (c) 30° (d) 145°
40. 40.Two angles of a triangle are 20° and 45°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 135° (d) 160°

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