Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 302 · 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 110°. What is each of the other two angles? (a) 45° (b) 110° (c) 35° (d) 70°
2. 2.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 150° (c) 120° (d) 60°
3. 3.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 20° (c) 55° (d) 70°
4. 4.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 140° (d) 160°
5. 5.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 140° (b) 80° (c) 100° (d) 280°
6. 6.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 220° (b) 40° (c) 41° (d) 140°
7. 7.Two angles of a triangle are 25° and 20°. What is the third angle? (a) 45° (b) 160° (c) 135° (d) 155°
8. 8.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 55° (c) 35° (d) 145°
9. 9.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 40° (c) 100° (d) 80°
10. 10.Two angles of a triangle are 55° and 60°. What is the third angle? (a) 115° (b) 65° (c) 120° (d) 125°
11. 11.Two angles of a triangle are 35° and 45°. What is the exterior angle at the third corner? (a) 80° (b) 135° (c) 145° (d) 100°
12. 12.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 30° (b) 75° (c) 135° (d) 150°
13. 13.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 70° (c) 125° (d) 55°
14. 14.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 120° (c) 30° (d) 60°
15. 15.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 170° (b) 20° (c) 10° (d) 11°
16. 16.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 36° (b) 70° (c) 35° (d) 145°
17. 17.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 165° (b) 110° (c) 85° (d) 15°
18. 18.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 160° (b) 340° (c) 70° (d) 20°
19. 19.Two angles of a triangle are 30° and 100°. What is the third angle? (a) 130° (b) 50° (c) 80° (d) 150°
20. 20.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 245° (b) 115° (c) 66° (d) 65°
21. 21.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 105° (b) 145° (c) 75° (d) 110°
22. 22.Two angles of a triangle are 45° and 85°. What is the third angle? (a) 50° (b) 135° (c) 95° (d) 130°
23. 23.Two angles of a triangle are 35° and 110°. What is the exterior angle at the third corner? (a) 215° (b) 145° (c) 35° (d) 70°
24. 24.Two angles of a triangle are 50° and 75°. What is the exterior angle at the third corner? (a) 55° (b) 130° (c) 105° (d) 125°
25. 25.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) 40° (d) 70°
26. 26.Two angles of a triangle are 30° and 55°. What is the third angle? (a) 150° (b) 85° (c) 95° (d) 125°
27. 27.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 100° (b) 51° (c) 50° (d) 130°
28. 28.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 59° (b) 60° (c) 61° (d) 120°
29. 29.Two angles of a triangle are 35° and 130°. What is the third angle? (a) 145° (b) 165° (c) 50° (d) 15°
30. 30.Two angles of a triangle are 25° and 70°. What is the third angle? (a) 85° (b) 95° (c) 155° (d) 110°
31. 31.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 65° (b) 50° (c) 115° (d) 230°
32. 32.Two angles of a triangle are 20° and 65°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 160° (d) 115°
33. 33.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 10° (b) 85° (c) 95° (d) 5°
34. 34.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 80° (b) 145° (c) 135° (d) 100°
35. 35.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 300° (b) 30° (c) 120° (d) 150°
36. 36.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 40° (c) 20° (d) 70°
37. 37.Two angles of a triangle are 35° and 115°. What is the third angle? (a) 65° (b) 145° (c) 30° (d) 150°
38. 38.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) 285° (c) 15° (d) 105°
39. 39.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 70° (b) 110° (c) 290° (d) 20°
40. 40.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 155° (b) 100° (c) 80° (d) 105°

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