Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 622 · 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 55° and 85°. What is the third angle? (a) 125° (b) 40° (c) 140° (d) 95°
2. 2.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 135° (c) 105° (d) 75°
3. 3.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 121° (b) 240° (c) 120° (d) 60°
4. 4.Two angles of a triangle are 40° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 75° (c) 140° (d) 105°
5. 5.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 35° (c) 55° (d) 110°
6. 6.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 120° (b) 30° (c) 90° (d) 150°
7. 7.Two angles of a triangle are 75° and 70°. What is the exterior angle at the third corner? (a) 35° (b) 105° (c) 110° (d) 145°
8. 8.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 190° (b) 10° (c) 85° (d) 95°
9. 9.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 40° (b) 130° (c) 310° (d) 50°
10. 10.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 110° (b) 250° (c) 140° (d) 70°
11. 11.Two angles of a triangle are 60° and 80°. What is the exterior angle at the third corner? (a) 120° (b) 100° (c) 40° (d) 140°
12. 12.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 110° (c) 70° (d) 20°
13. 13.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 140° (b) 10° (c) 170° (d) 50°
14. 14.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°
15. 15.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 11° (b) 20° (c) 170° (d) 10°
16. 16.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 50° (c) 100° (d) 140°
17. 17.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 35° (b) 145° (c) 290° (d) 110°
18. 18.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 100° (c) 140° (d) 280°
19. 19.Two angles of a triangle are 45° and 35°. What is the third angle? (a) 80° (b) 145° (c) 135° (d) 100°
20. 20.Two angles of a triangle are 80° and 85°. What is the third angle? (a) 165° (b) 95° (c) 15° (d) 100°
21. 21.Two angles of a triangle are 35° and 135°. What is the third angle? (a) 170° (b) 45° (c) 145° (d) 10°
22. 22.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 120° (b) 105° (c) 135° (d) 75°
23. 23.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 340° (b) 20° (c) 70° (d) 160°
24. 24.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 70° (c) 105° (d) 110°
25. 25.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 235° (b) 56° (c) 125° (d) 55°
26. 26.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 95° (c) 170° (d) 86°
27. 27.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) 20° (c) 70° (d) 290°
28. 28.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 50° (c) 40° (d) 80°
29. 29.Two angles of a triangle are 25° and 125°. What is the exterior angle at the third corner? (a) 155° (b) 55° (c) 30° (d) 150°
30. 30.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 25° (b) 100° (c) 105° (d) 155°
31. 31.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 110° (c) 70° (d) 35°
32. 32.Two angles of a triangle are 80° and 45°. What is the exterior angle at the third corner? (a) 55° (b) 100° (c) 125° (d) 135°
33. 33.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 120° (c) 150° (d) 30°
34. 34.Two angles of a triangle are 75° and 60°. What is the exterior angle at the third corner? (a) 135° (b) 120° (c) 105° (d) 45°
35. 35.Two angles of a triangle are 75° and 55°. What is the exterior angle at the third corner? (a) 50° (b) 130° (c) 125° (d) 105°
36. 36.Two angles of a triangle are 35° and 20°. What is the third angle? (a) 125° (b) 55° (c) 160° (d) 145°
37. 37.Two angles of a triangle are 40° and 105°. What is the exterior angle at the third corner? (a) 145° (b) 140° (c) 35° (d) 75°
38. 38.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 60° (b) 100° (c) 140° (d) 120°
39. 39.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 91° (c) 90° (d) 45°
40. 40.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 60° (b) 30° (c) 120° (d) 40°

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