Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 187 · 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 straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 220° (b) 110° (c) 40° (d) 70°
2. 2.Two angles of a triangle are 30° and 30°. What is the exterior angle at the third corner? (a) 300° (b) 150° (c) 60° (d) 120°
3. 3.Two angles of a triangle are 30° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 105° (c) 150° (d) 75°
4. 4.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 75° (b) 150° (c) 135° (d) 105°
5. 5.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 50° (c) 40° (d) 100°
6. 6.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) 30° (d) 150°
7. 7.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 85° (b) 160° (c) 95° (d) 115°
8. 8.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 60° (b) 240° (c) 120° (d) 121°
9. 9.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 140° (b) 70° (c) 110° (d) 71°
10. 10.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 105° (b) 155° (c) 100° (d) 75°
11. 11.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°
12. 12.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 95° (c) 85° (d) 10°
13. 13.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 110° (b) 80° (c) 150° (d) 100°
14. 14.Two angles of a triangle are 35° and 55°. What is the third angle? (a) 145° (b) 270° (c) 125° (d) 90°
15. 15.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 40° (b) 140° (c) 320° (d) 50°
16. 16.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 50° (c) 80° (d) 100°
17. 17.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°
18. 18.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°
19. 19.Two angles of a triangle are 50° and 105°. What is the third angle? (a) 130° (b) 155° (c) 75° (d) 25°
20. 20.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 75° (c) 30° (d) 105°
21. 21.Two angles of a triangle are 40° and 65°. What is the exterior angle at the third corner? (a) 75° (b) 140° (c) 115° (d) 105°
22. 22.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 130° (b) 50° (c) 80° (d) 260°
23. 23.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 85° (b) 145° (c) 120° (d) 95°
24. 24.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 130° (c) 155° (d) 65°
25. 25.Two angles of a triangle are 70° and 75°. What is the exterior angle at the third corner? (a) 145° (b) 35° (c) 110° (d) 105°
26. 26.Two angles of a triangle are 45° and 125°. What is the third angle? (a) 55° (b) 135° (c) 170° (d) 10°
27. 27.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 40° (c) 20° (d) 110°
28. 28.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 80° (c) 70° (d) 160°
29. 29.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°
30. 30.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 46° (b) 45° (c) 135° (d) 90°
31. 31.Two angles of a triangle are 20° and 105°. What is the third angle? (a) 160° (b) 55° (c) 125° (d) 75°
32. 32.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 25° (c) 50° (d) 130°
33. 33.Two angles of a triangle are 20° and 75°. What is the third angle? (a) 95° (b) 160° (c) 105° (d) 85°
34. 34.Two angles of a triangle are 35° and 70°. What is the third angle? (a) 145° (b) 105° (c) 110° (d) 75°
35. 35.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 145° (c) 150° (d) 65°
36. 36.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 235° (b) 56° (c) 55° (d) 125°
37. 37.Two angles of a triangle are 45° and 35°. What is the exterior angle at the third corner? (a) 100° (b) 135° (c) 80° (d) 145°
38. 38.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 280° (b) 140° (c) 80° (d) 100°
39. 39.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 140° (c) 50° (d) 70°
40. 40.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 70° (c) 110° (d) 290°

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