Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 116 · 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) 25° (b) 30° (c) 150° (d) 15°
2. 2.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 170° (c) 95° (d) 85°
3. 3.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 110° (d) 145°
4. 4.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 55° (c) 20° (d) 70°
5. 5.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 120° (c) 150° (d) 60°
6. 6.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 260° (b) 130° (c) 80° (d) 50°
7. 7.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 85° (b) 5° (c) 95° (d) 275°
8. 8.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 65° (c) 40° (d) 130°
9. 9.Two angles of a triangle are 55° and 20°. What is the third angle? (a) 125° (b) 75° (c) 105° (d) 160°
10. 10.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 115° (b) 135° (c) 70° (d) 110°
11. 11.Two angles of a triangle are 45° and 20°. What is the exterior angle at the third corner? (a) 115° (b) 160° (c) 135° (d) 65°
12. 12.Two angles of a triangle are 50° and 45°. What is the third angle? (a) 85° (b) 130° (c) 95° (d) 135°
13. 13.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 290° (d) 145°
14. 14.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 110° (b) 290° (c) 20° (d) 70°
15. 15.Two angles of a triangle are 25° and 95°. What is the exterior angle at the third corner? (a) 120° (b) 155° (c) 85° (d) 60°
16. 16.Two angles of a triangle are 40° and 30°. What is the exterior angle at the third corner? (a) 140° (b) 150° (c) 110° (d) 70°
17. 17.Two angles of a triangle are 45° and 100°. What is the exterior angle at the third corner? (a) 35° (b) 145° (c) 80° (d) 135°
18. 18.Two angles of a triangle are 20° and 80°. What is the third angle? (a) 260° (b) 100° (c) 160° (d) 80°
19. 19.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 60° (c) 30° (d) 150°
20. 20.Two angles of a triangle are 35° and 130°. What is the third angle? (a) 145° (b) 165° (c) 50° (d) 15°
21. 21.Two angles of a triangle are 25° and 115°. What is the exterior angle at the third corner? (a) 40° (b) 140° (c) 65° (d) 155°
22. 22.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) 255° (d) 75°
23. 23.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 100° (b) 125° (c) 135° (d) 45°
24. 24.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 110° (b) 150° (c) 80° (d) 100°
25. 25.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 25° (c) 155° (d) 130°
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 angles of a triangle are 40° and 30°. What is the third angle? (a) 70° (b) 140° (c) 110° (d) 150°
28. 28.Two angles of a triangle are 65° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 110° (c) 115° (d) 70°
29. 29.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 145° (b) 110° (c) 35° (d) 105°
30. 30.Two angles of a triangle are 60° and 70°. What is the exterior angle at the third corner? (a) 120° (b) 130° (c) 110° (d) 50°
31. 31.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 145° (c) 80° (d) 100°
32. 32.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 70° (c) 80° (d) 160°
33. 33.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°
34. 34.Two angles of a triangle are 30° and 110°. What is the exterior angle at the third corner? (a) 70° (b) 40° (c) 140° (d) 150°
35. 35.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 25° (b) 130° (c) 310° (d) 155°
36. 36.Two angles of a triangle are 40° and 50°. What is the third angle? (a) 140° (b) 130° (c) 270° (d) 90°
37. 37.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 85° (c) 5° (d) 10°
38. 38.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 45° (c) 70° (d) 110°
39. 39.Two angles of a triangle are 65° and 85°. What is the third angle? (a) 115° (b) 30° (c) 95° (d) 150°
40. 40.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 125° (b) 25° (c) 155° (d) 80°

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