Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 11 · 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 110°. What is each of the other two angles? (a) 125° (b) 55° (c) 70° (d) 250°
2. 2.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 95° (c) 265° (d) 86°
3. 3.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 90° (c) 91° (d) 45°
4. 4.Two angles of a triangle are 60° and 80°. What is the third angle? (a) 120° (b) 100° (c) 140° (d) 40°
5. 5.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 115° (b) 230° (c) 65° (d) 50°
6. 6.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 65° (b) 115° (c) 66° (d) 245°
7. 7.Two angles of a triangle are 25° and 50°. What is the third angle? (a) 75° (b) 130° (c) 105° (d) 155°
8. 8.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 45° (b) 125° (c) 100° (d) 135°
9. 9.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 61° (c) 120° (d) 30°
10. 10.Two angles of a triangle are 45° and 110°. What is the third angle? (a) 155° (b) 25° (c) 135° (d) 70°
11. 11.Two angles of a triangle are 30° and 35°. What is the third angle? (a) 150° (b) 65° (c) 145° (d) 115°
12. 12.Two angles of a triangle are 35° and 30°. What is the exterior angle at the third corner? (a) 145° (b) 150° (c) 65° (d) 115°
13. 13.Two angles of a triangle are 50° and 105°. What is the third angle? (a) 25° (b) 130° (c) 155° (d) 75°
14. 14.Two angles of a triangle are 60° and 70°. What is the exterior angle at the third corner? (a) 120° (b) 130° (c) 110° (d) 50°
15. 15.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) 50° (d) 70°
16. 16.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 140° (b) 75° (c) 145° (d) 105°
17. 17.Two angles of a triangle are 30° and 120°. What is the exterior angle at the third corner? (a) 30° (b) 60° (c) 210° (d) 150°
18. 18.Two angles of a triangle are 30° and 95°. What is the exterior angle at the third corner? (a) 55° (b) 150° (c) 85° (d) 125°
19. 19.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 140° (b) 280° (c) 40° (d) 100°
20. 20.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 105° (b) 110° (c) 75° (d) 145°
21. 21.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 130° (b) 140° (c) 90° (d) 270°
22. 22.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 110° (b) 55° (c) 125° (d) 235°
23. 23.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) 80° (d) 100°
24. 24.Two angles of a triangle are 60° and 75°. What is the third angle? (a) 135° (b) 105° (c) 45° (d) 120°
25. 25.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 55° (b) 70° (c) 110° (d) 20°
26. 26.Two angles of a triangle are 80° and 50°. What is the third angle? (a) 230° (b) 50° (c) 130° (d) 100°
27. 27.Two angles of a triangle are 35° and 115°. What is the third angle? (a) 65° (b) 150° (c) 30° (d) 145°
28. 28.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 105° (b) 145° (c) 110° (d) 70°
29. 29.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 55° (b) 145° (c) 35° (d) 325°
30. 30.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 125° (b) 55° (c) 56° (d) 235°
31. 31.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 310° (b) 25° (c) 130° (d) 155°
32. 32.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 30° (b) 110° (c) 150° (d) 100°
33. 33.Two angles of a triangle are 20° and 100°. What is the third angle? (a) 160° (b) 120° (c) 60° (d) 80°
34. 34.Two angles of a triangle are 20° and 90°. What is the exterior angle at the third corner? (a) 160° (b) 70° (c) 90° (d) 110°
35. 35.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 255° (b) 76° (c) 75° (d) 105°
36. 36.Two angles of a triangle are 75° and 55°. What is the exterior angle at the third corner? (a) 50° (b) 105° (c) 130° (d) 125°
37. 37.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 90° (b) 45° (c) 270° (d) 135°
38. 38.Two angles of a triangle are 45° and 55°. What is the third angle? (a) 135° (b) 80° (c) 125° (d) 100°
39. 39.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 95° (c) 85° (d) 86°
40. 40.Two angles of a triangle are 45° and 90°. What is the third angle? (a) 135° (b) 90° (c) 45° (d) 225°

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