Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 399 · 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 170°. What is each of the other two angles? (a) 85° (b) 10° (c) 95° (d) 190°
2. 2.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 100° (b) 120° (c) 80° (d) 140°
3. 3.Two angles of a triangle are 30° and 90°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 90° (d) 150°
4. 4.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 60° (b) 30° (c) 150° (d) 330°
5. 5.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 275° (b) 85° (c) 5° (d) 95°
6. 6.Two angles of a triangle are 55° and 110°. What is the third angle? (a) 125° (b) 15° (c) 70° (d) 165°
7. 7.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 120° (c) 60° (d) 30°
8. 8.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 270° (b) 135° (c) 45° (d) 90°
9. 9.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 50° (b) 130° (c) 51° (d) 230°
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 angles of a triangle are 70° and 75°. What is the third angle? (a) 110° (b) 105° (c) 35° (d) 145°
12. 12.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 145° (c) 55° (d) 110°
13. 13.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 25° (c) 15° (d) 150°
14. 14.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) 45° (c) 136° (d) 135°
15. 15.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 20° (c) 140° (d) 30°
16. 16.Two angles of a triangle are 35° and 85°. What is the exterior angle at the third corner? (a) 60° (b) 145° (c) 95° (d) 120°
17. 17.Two angles of a triangle are 55° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 30° (c) 150° (d) 125°
18. 18.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 50° (c) 65° (d) 40°
19. 19.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 135° (b) 70° (c) 110° (d) 115°
20. 20.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 15° (b) 30° (c) 16° (d) 165°
21. 21.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 60° (c) 75° (d) 150°
22. 22.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 30° (b) 210° (c) 75° (d) 105°
23. 23.Two angles of a triangle are 20° and 105°. What is the exterior angle at the third corner? (a) 125° (b) 55° (c) 75° (d) 160°
24. 24.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) 105° (d) 150°
25. 25.Two angles of a triangle are 35° and 30°. What is the exterior angle at the third corner? (a) 115° (b) 150° (c) 145° (d) 65°
26. 26.Two angles of a triangle are 20° and 115°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 65° (d) 160°
27. 27.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 140° (c) 40° (d) 100°
28. 28.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 155° (d) 145°
29. 29.Two angles of a triangle are 75° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 50° (c) 105° (d) 130°
30. 30.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 55° (b) 145° (c) 35° (d) 325°
31. 31.Two angles of a triangle are 60° and 100°. What is the third angle? (a) 120° (b) 20° (c) 80° (d) 160°
32. 32.Two angles of a triangle are 65° and 95°. What is the third angle? (a) 85° (b) 20° (c) 115° (d) 160°
33. 33.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°
34. 34.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 145° (b) 105° (c) 140° (d) 75°
35. 35.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 50° (b) 160° (c) 150° (d) 20°
36. 36.Two angles of a triangle are 50° and 115°. What is the third angle? (a) 165° (b) 130° (c) 15° (d) 65°
37. 37.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°
38. 38.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 10° (c) 11° (d) 20°
39. 39.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 60° (c) 70° (d) 30°
40. 40.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 130° (c) 155° (d) 65°

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