Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 36 · 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 160°. What is each of the other two angles? (a) 10° (b) 11° (c) 20° (d) 160°
2. 2.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 50° (c) 70° (d) 40°
3. 3.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 30° (b) 31° (c) 150° (d) 60°
4. 4.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 50° (b) 320° (c) 140° (d) 40°
5. 5.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 230° (c) 130° (d) 50°
6. 6.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 55° (b) 235° (c) 56° (d) 125°
7. 7.Two angles of a triangle are 40° and 90°. What is the exterior angle at the third corner? (a) 140° (b) 130° (c) 50° (d) 90°
8. 8.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 260° (c) 100° (d) 80°
9. 9.Two angles of a triangle are 65° and 65°. What is the third angle? (a) 115° (b) 130° (c) 230° (d) 50°
10. 10.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 105° (b) 145° (c) 110° (d) 35°
11. 11.Two angles of a triangle are 40° and 105°. What is the exterior angle at the third corner? (a) 35° (b) 140° (c) 145° (d) 75°
12. 12.Two angles of a triangle are 55° and 75°. What is the exterior angle at the third corner? (a) 50° (b) 125° (c) 130° (d) 105°
13. 13.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 25° (c) 30° (d) 15°
14. 14.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 51° (b) 130° (c) 50° (d) 100°
15. 15.Two angles of a triangle are 65° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 115° (c) 120° (d) 60°
16. 16.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 260° (b) 81° (c) 100° (d) 80°
17. 17.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 20° (c) 160° (d) 80°
18. 18.Two angles of a triangle are 40° and 75°. What is the third angle? (a) 105° (b) 140° (c) 115° (d) 65°
19. 19.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 35° (c) 110° (d) 55°
20. 20.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°
21. 21.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 45° (b) 136° (c) 135° (d) 315°
22. 22.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 110° (b) 80° (c) 150° (d) 100°
23. 23.Two angles of a triangle are 75° and 60°. What is the exterior angle at the third corner? (a) 105° (b) 135° (c) 120° (d) 45°
24. 24.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 70° (c) 20° (d) 40°
25. 25.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 145° (b) 125° (c) 160° (d) 55°
26. 26.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 115° (b) 65° (c) 66° (d) 245°
27. 27.Two angles of a triangle are 40° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 55° (c) 140° (d) 125°
28. 28.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 35° (c) 70° (d) 125°
29. 29.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 45° (b) 135° (c) 90° (d) 270°
30. 30.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 140° (c) 50° (d) 100°
31. 31.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 110° (b) 100° (c) 150° (d) 70°
32. 32.Two angles of a triangle are 80° and 50°. What is the exterior angle at the third corner? (a) 230° (b) 130° (c) 100° (d) 50°
33. 33.Two angles of a triangle are 25° and 115°. What is the third angle? (a) 155° (b) 65° (c) 140° (d) 40°
34. 34.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 155° (c) 130° (d) 25°
35. 35.Two angles of a triangle are 60° and 20°. What is the exterior angle at the third corner? (a) 120° (b) 100° (c) 80° (d) 160°
36. 36.Two angles of a triangle are 50° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 80° (c) 100° (d) 260°
37. 37.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 16° (b) 165° (c) 30° (d) 15°
38. 38.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 135° (c) 150° (d) 30°
39. 39.Two angles of a triangle are 30° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 150° (d) 255°
40. 40.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°

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