Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 71 · 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 angles of a triangle are 65° and 30°. What is the third angle? (a) 115° (b) 150° (c) 95° (d) 85°
2. 2.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) 66° (d) 65°
3. 3.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 40° (b) 220° (c) 110° (d) 70°
4. 4.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 61° (c) 30° (d) 120°
5. 5.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 230° (b) 51° (c) 50° (d) 130°
6. 6.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 50° (b) 230° (c) 65° (d) 115°
7. 7.Two angles of a triangle are 30° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 110° (c) 70° (d) 150°
8. 8.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 165° (b) 16° (c) 15° (d) 195°
9. 9.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 160° (b) 200° (c) 21° (d) 20°
10. 10.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 130° (b) 50° (c) 120° (d) 110°
11. 11.Two angles of a triangle are 50° and 95°. What is the third angle? (a) 145° (b) 35° (c) 130° (d) 85°
12. 12.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 70° (c) 140° (d) 50°
13. 13.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 70° (c) 110° (d) 130°
14. 14.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 70° (c) 110° (d) 45°
15. 15.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 15° (b) 16° (c) 165° (d) 30°
16. 16.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 75° (b) 15° (c) 285° (d) 105°
17. 17.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 135° (b) 80° (c) 145° (d) 100°
18. 18.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 20° (b) 110° (c) 70° (d) 290°
19. 19.Two angles of a triangle are 55° and 55°. What is the third angle? (a) 110° (b) 125° (c) 70° (d) 250°
20. 20.Two angles of a triangle are 80° and 20°. What is the third angle? (a) 160° (b) 260° (c) 100° (d) 80°
21. 21.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 55° (c) 90° (d) 46°
22. 22.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 55° (c) 35° (d) 145°
23. 23.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 130° (c) 50° (d) 25°
24. 24.Two angles of a triangle are 70° and 20°. What is the third angle? (a) 90° (b) 270° (c) 110° (d) 160°
25. 25.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 20° (c) 80° (d) 100°
26. 26.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 60° (c) 120° (d) 30°
27. 27.Two angles of a triangle are 20° and 120°. What is the exterior angle at the third corner? (a) 40° (b) 160° (c) 60° (d) 140°
28. 28.Two angles of a triangle are 50° and 80°. What is the third angle? (a) 100° (b) 130° (c) 230° (d) 50°
29. 29.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 26° (b) 25° (c) 50° (d) 155°
30. 30.Two angles of a triangle are 70° and 70°. What is the exterior angle at the third corner? (a) 40° (b) 110° (c) 220° (d) 140°
31. 31.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 110° (b) 35° (c) 145° (d) 290°
32. 32.Two angles of a triangle are 40° and 105°. What is the third angle? (a) 145° (b) 140° (c) 75° (d) 35°
33. 33.Two angles of a triangle are 55° and 85°. What is the exterior angle at the third corner? (a) 140° (b) 95° (c) 40° (d) 125°
34. 34.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 120° (b) 125° (c) 60° (d) 115°
35. 35.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 145° (c) 60° (d) 120°
36. 36.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 155° (c) 25° (d) 130°
37. 37.Two angles of a triangle are 20° and 80°. What is the exterior angle at the third corner? (a) 260° (b) 100° (c) 80° (d) 160°
38. 38.Two angles of a triangle are 20° and 40°. What is the third angle? (a) 160° (b) 60° (c) 120° (d) 140°
39. 39.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 135° (c) 100° (d) 45°
40. 40.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) 70° (d) 20°

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