Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 294 · 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 150°. What is each of the other two angles? (a) 15° (b) 25° (c) 30° (d) 150°
2. 2.Two angles of a triangle are 25° and 90°. What is the exterior angle at the third corner? (a) 115° (b) 90° (c) 155° (d) 65°
3. 3.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 65° (c) 25° (d) 50°
4. 4.Two angles of a triangle are 40° and 50°. What is the third angle? (a) 140° (b) 270° (c) 90° (d) 130°
5. 5.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 130° (b) 160° (c) 70° (d) 110°
6. 6.Two angles of a triangle are 60° and 50°. What is the third angle? (a) 70° (b) 110° (c) 120° (d) 130°
7. 7.Two angles of a triangle are 40° and 80°. What is the third angle? (a) 60° (b) 140° (c) 120° (d) 100°
8. 8.Two angles of a triangle are 60° and 55°. What is the third angle? (a) 125° (b) 115° (c) 65° (d) 120°
9. 9.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 30° (c) 60° (d) 70°
10. 10.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 115° (b) 130° (c) 65° (d) 66°
11. 11.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 110° (c) 40° (d) 20°
12. 12.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 71° (b) 70° (c) 250° (d) 110°
13. 13.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 140° (b) 80° (c) 41° (d) 40°
14. 14.Two angles of a triangle are 70° and 65°. What is the exterior angle at the third corner? (a) 135° (b) 110° (c) 45° (d) 115°
15. 15.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 125° (b) 70° (c) 250° (d) 55°
16. 16.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 150° (b) 31° (c) 30° (d) 60°
17. 17.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 76° (b) 105° (c) 75° (d) 255°
18. 18.Two angles of a triangle are 35° and 105°. What is the third angle? (a) 140° (b) 145° (c) 40° (d) 75°
19. 19.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 40° (c) 50° (d) 80°
20. 20.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 45° (c) 135° (d) 115°
21. 21.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 130° (c) 80° (d) 40°
22. 22.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 100° (b) 115° (c) 65° (d) 145°
23. 23.Two angles of a triangle are 60° and 95°. What is the third angle? (a) 85° (b) 120° (c) 155° (d) 25°
24. 24.Two angles of a triangle are 20° and 20°. What is the third angle? (a) 40° (b) 320° (c) 160° (d) 140°
25. 25.Two angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 65° (b) 140° (c) 155° (d) 115°
26. 26.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) 50° (c) 130° (d) 40°
27. 27.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 11° (b) 170° (c) 10° (d) 190°
28. 28.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 55° (b) 35° (c) 125° (d) 305°
29. 29.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) 110° (d) 55°
30. 30.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 50° (c) 10° (d) 100°
31. 31.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) 86° (c) 85° (d) 265°
32. 32.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°
33. 33.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 135° (b) 160° (c) 155° (d) 45°
34. 34.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 35° (c) 130° (d) 25°
35. 35.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 110° (c) 35° (d) 55°
36. 36.Two angles of a triangle are 65° and 60°. What is the third angle? (a) 125° (b) 115° (c) 120° (d) 55°
37. 37.Two angles of a triangle are 80° and 90°. What is the third angle? (a) 90° (b) 10° (c) 170° (d) 100°
38. 38.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 85° (b) 10° (c) 170° (d) 105°
39. 39.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 335° (b) 25° (c) 65° (d) 155°
40. 40.Two angles of a triangle are 35° and 120°. What is the third angle? (a) 25° (b) 145° (c) 155° (d) 60°

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