Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 284 · 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 20° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 320° (c) 140° (d) 40°
2. 2.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 25° (c) 65° (d) 130°
3. 3.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 145° (b) 110° (c) 35° (d) 290°
4. 4.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°
5. 5.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) 66° (c) 65° (d) 115°
6. 6.Two angles of a triangle are 30° and 110°. What is the third angle? (a) 140° (b) 40° (c) 70° (d) 150°
7. 7.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 125° (c) 70° (d) 35°
8. 8.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 100° (c) 50° (d) 80°
9. 9.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 130° (c) 35° (d) 25°
10. 10.Two angles of a triangle are 35° and 85°. What is the exterior angle at the third corner? (a) 120° (b) 95° (c) 145° (d) 60°
11. 11.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 40° (b) 140° (c) 41° (d) 80°
12. 12.Two angles of a triangle are 30° and 65°. What is the third angle? (a) 150° (b) 115° (c) 95° (d) 85°
13. 13.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 100° (b) 280° (c) 80° (d) 10°
14. 14.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 160° (c) 80° (d) 70°
15. 15.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 50° (c) 100° (d) 40°
16. 16.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 65° (b) 335° (c) 25° (d) 155°
17. 17.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 270° (b) 45° (c) 135° (d) 90°
18. 18.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 71° (b) 110° (c) 250° (d) 70°
19. 19.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 120° (b) 240° (c) 121° (d) 60°
20. 20.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 35° (b) 65° (c) 145° (d) 150°
21. 21.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 100° (b) 160° (c) 80° (d) 260°
22. 22.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 10° (c) 100° (d) 20°
23. 23.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 160° (b) 20° (c) 150° (d) 50°
24. 24.Two angles of a triangle are 60° and 30°. What is the exterior angle at the third corner? (a) 90° (b) 120° (c) 270° (d) 150°
25. 25.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 81° (b) 100° (c) 160° (d) 80°
26. 26.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 140° (c) 30° (d) 20°
27. 27.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 75° (b) 155° (c) 105° (d) 130°
28. 28.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 70° (c) 20° (d) 110°
29. 29.Two angles of a triangle are 25° and 85°. What is the exterior angle at the third corner? (a) 70° (b) 95° (c) 155° (d) 110°
30. 30.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 40° (c) 70° (d) 50°
31. 31.Two angles of a triangle are 25° and 120°. What is the third angle? (a) 35° (b) 60° (c) 145° (d) 155°
32. 32.Two angles of a triangle are 20° and 70°. What is the third angle? (a) 160° (b) 110° (c) 270° (d) 90°
33. 33.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 80° (c) 130° (d) 260°
34. 34.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 60° (c) 150° (d) 120°
35. 35.Two angles of a triangle are 65° and 90°. What is the third angle? (a) 25° (b) 155° (c) 90° (d) 115°
36. 36.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 60° (b) 240° (c) 61° (d) 120°
37. 37.Two angles of a triangle are 20° and 35°. What is the exterior angle at the third corner? (a) 125° (b) 145° (c) 160° (d) 55°
38. 38.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 60° (c) 70° (d) 120°
39. 39.Two angles of a triangle are 55° and 80°. What is the exterior angle at the third corner? (a) 125° (b) 100° (c) 45° (d) 135°
40. 40.Two angles of a triangle are 25° and 100°. What is the third angle? (a) 125° (b) 80° (c) 55° (d) 155°

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