Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 345 · 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. 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°
2. 2.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 145° (d) 110°
3. 3.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 80° (c) 40° (d) 130°
4. 4.Two angles of a triangle are 20° and 30°. What is the third angle? (a) 130° (b) 50° (c) 160° (d) 150°
5. 5.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 40° (c) 50° (d) 70°
6. 6.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 155° (c) 130° (d) 25°
7. 7.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 30° (b) 210° (c) 105° (d) 150°
8. 8.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 70° (b) 340° (c) 160° (d) 20°
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) 15° (c) 16° (d) 165°
10. 10.Two angles of a triangle are 40° and 30°. What is the third angle? (a) 70° (b) 110° (c) 150° (d) 140°
11. 11.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 136° (b) 45° (c) 315° (d) 135°
12. 12.Two angles of a triangle are 55° and 50°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 125° (d) 130°
13. 13.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 40° (b) 105° (c) 115° (d) 140°
14. 14.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 30° (b) 120° (c) 40° (d) 60°
15. 15.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 105° (b) 145° (c) 140° (d) 75°
16. 16.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) 40° (c) 130° (d) 50°
17. 17.Two angles of a triangle are 20° and 115°. What is the exterior angle at the third corner? (a) 45° (b) 160° (c) 65° (d) 135°
18. 18.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 150° (b) 330° (c) 30° (d) 60°
19. 19.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 90° (b) 135° (c) 45° (d) 270°
20. 20.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 100° (c) 20° (d) 10°
21. 21.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 30° (c) 120° (d) 150°
22. 22.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 30° (c) 75° (d) 15°
23. 23.Two angles of a triangle are 65° and 45°. What is the exterior angle at the third corner? (a) 115° (b) 110° (c) 135° (d) 70°
24. 24.Two angles of a triangle are 30° and 85°. What is the exterior angle at the third corner? (a) 150° (b) 65° (c) 115° (d) 95°
25. 25.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 110° (c) 35° (d) 45°
26. 26.Two angles of a triangle are 60° and 100°. What is the third angle? (a) 120° (b) 80° (c) 20° (d) 160°
27. 27.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 90° (b) 135° (c) 45° (d) 46°
28. 28.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 105° (c) 110° (d) 70°
29. 29.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 105° (b) 210° (c) 30° (d) 75°
30. 30.Two angles of a triangle are 20° and 110°. What is the exterior angle at the third corner? (a) 130° (b) 70° (c) 160° (d) 50°
31. 31.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 100° (b) 80° (c) 10° (d) 280°
32. 32.Two angles of a triangle are 45° and 55°. What is the third angle? (a) 125° (b) 100° (c) 80° (d) 135°
33. 33.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 65° (c) 25° (d) 50°
34. 34.Two angles of a triangle are 20° and 85°. What is the third angle? (a) 160° (b) 75° (c) 95° (d) 105°
35. 35.Two angles of a triangle are 55° and 45°. What is the exterior angle at the third corner? (a) 125° (b) 135° (c) 80° (d) 100°
36. 36.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 105° (b) 145° (c) 75° (d) 110°
37. 37.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 155° (b) 25° (c) 26° (d) 50°
38. 38.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 145° (b) 110° (c) 75° (d) 105°
39. 39.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 56° (b) 55° (c) 125° (d) 235°
40. 40.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 40° (c) 110° (d) 20°

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