Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 60 · 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. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 170° (b) 11° (c) 10° (d) 20°
2. 2.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 20° (b) 40° (c) 21° (d) 160°
3. 3.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 120° (b) 300° (c) 150° (d) 30°
4. 4.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 50° (c) 40° (d) 100°
5. 5.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) 50° (d) 140°
6. 6.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 100° (c) 115° (d) 65°
7. 7.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°
8. 8.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 150° (c) 60° (d) 30°
9. 9.Two angles of a triangle are 35° and 75°. What is the third angle? (a) 105° (b) 70° (c) 110° (d) 145°
10. 10.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 60° (b) 140° (c) 120° (d) 100°
11. 11.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 55° (c) 70° (d) 110°
12. 12.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 155° (b) 26° (c) 205° (d) 25°
13. 13.Two angles of a triangle are 20° and 150°. What is the third angle? (a) 10° (b) 170° (c) 30° (d) 160°
14. 14.Two angles of a triangle are 50° and 75°. What is the third angle? (a) 105° (b) 130° (c) 55° (d) 125°
15. 15.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 280° (b) 10° (c) 100° (d) 80°
16. 16.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 20° (c) 110° (d) 40°
17. 17.Two angles of a triangle are 35° and 20°. What is the third angle? (a) 160° (b) 125° (c) 55° (d) 145°
18. 18.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 35° (c) 70° (d) 55°
19. 19.Two angles of a triangle are 30° and 40°. What is the exterior angle at the third corner? (a) 110° (b) 150° (c) 140° (d) 70°
20. 20.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 105° (c) 15° (d) 30°
21. 21.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 135° (b) 46° (c) 225° (d) 45°
22. 22.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 125° (b) 55° (c) 305° (d) 35°
23. 23.Two angles of a triangle are 65° and 75°. What is the third angle? (a) 115° (b) 105° (c) 140° (d) 40°
24. 24.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 125° (b) 55° (c) 120° (d) 115°
25. 25.Two angles of a triangle are 75° and 60°. What is the exterior angle at the third corner? (a) 105° (b) 120° (c) 135° (d) 45°
26. 26.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 140° (b) 75° (c) 105° (d) 145°
27. 27.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 240° (b) 121° (c) 120° (d) 60°
28. 28.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 50° (c) 100° (d) 140°
29. 29.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 45° (b) 110° (c) 135° (d) 115°
30. 30.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 130° (c) 50° (d) 80°
31. 31.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 125° (b) 110° (c) 235° (d) 55°
32. 32.Two angles of a triangle are 20° and 30°. What is the third angle? (a) 50° (b) 150° (c) 160° (d) 130°
33. 33.Two angles of a triangle are 65° and 60°. What is the third angle? (a) 55° (b) 120° (c) 115° (d) 125°
34. 34.Two angles of a triangle are 70° and 50°. What is the third angle? (a) 130° (b) 60° (c) 110° (d) 120°
35. 35.Two angles of a triangle are 25° and 100°. What is the third angle? (a) 80° (b) 55° (c) 125° (d) 155°
36. 36.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 155° (c) 130° (d) 65°
37. 37.Two angles of a triangle are 35° and 65°. What is the exterior angle at the third corner? (a) 100° (b) 115° (c) 145° (d) 80°
38. 38.Two angles of a triangle are 40° and 95°. What is the exterior angle at the third corner? (a) 45° (b) 85° (c) 135° (d) 140°
39. 39.Two angles of a triangle are 60° and 65°. What is the third angle? (a) 115° (b) 125° (c) 55° (d) 120°
40. 40.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 61° (b) 240° (c) 60° (d) 120°

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