Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 26 · 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. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 45° (b) 225° (c) 135° (d) 46°
2. 2.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 136° (b) 315° (c) 135° (d) 45°
3. 3.Two angles of a triangle are 60° and 60°. What is the third angle? (a) 240° (b) 60° (c) 61° (d) 120°
4. 4.Two angles of a triangle are 45° and 55°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 125° (d) 135°
5. 5.Two angles of a triangle are 20° and 130°. What is the exterior angle at the third corner? (a) 150° (b) 160° (c) 50° (d) 30°
6. 6.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 85° (c) 95° (d) 86°
7. 7.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) 70° (c) 340° (d) 20°
8. 8.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 60° (c) 30° (d) 70°
9. 9.Two angles of a triangle are 20° and 20°. What is the third angle? (a) 320° (b) 140° (c) 160° (d) 40°
10. 10.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 110° (b) 290° (c) 145° (d) 35°
11. 11.Two angles of a triangle are 70° and 65°. What is the exterior angle at the third corner? (a) 135° (b) 115° (c) 110° (d) 45°
12. 12.Two angles of a triangle are 55° and 85°. What is the third angle? (a) 95° (b) 40° (c) 140° (d) 125°
13. 13.Two angles of a triangle are 45° and 85°. What is the exterior angle at the third corner? (a) 135° (b) 50° (c) 130° (d) 95°
14. 14.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 125° (b) 35° (c) 145° (d) 90°
15. 15.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 50° (b) 310° (c) 40° (d) 130°
16. 16.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 55° (b) 115° (c) 125° (d) 120°
17. 17.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 110° (b) 120° (c) 70° (d) 130°
18. 18.Two angles of a triangle are 30° and 110°. What is the third angle? (a) 140° (b) 150° (c) 40° (d) 70°
19. 19.Two angles of a triangle are 50° and 55°. What is the third angle? (a) 105° (b) 125° (c) 130° (d) 75°
20. 20.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°
21. 21.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 75° (b) 150° (c) 76° (d) 105°
22. 22.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 150° (b) 135° (c) 30° (d) 75°
23. 23.Two angles of a triangle are 30° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 50° (c) 150° (d) 130°
24. 24.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 20° (b) 10° (c) 100° (d) 80°
25. 25.Two angles of a triangle are 60° and 65°. What is the third angle? (a) 115° (b) 125° (c) 55° (d) 120°
26. 26.Two angles of a triangle are 80° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 100° (c) 55° (d) 125°
27. 27.Two angles of a triangle are 55° and 35°. What is the exterior angle at the third corner? (a) 90° (b) 270° (c) 125° (d) 145°
28. 28.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 35° (b) 305° (c) 55° (d) 125°
29. 29.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 40° (c) 50° (d) 65°
30. 30.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 65° (c) 25° (d) 50°
31. 31.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 35° (c) 110° (d) 45°
32. 32.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 10° (b) 85° (c) 5° (d) 95°
33. 33.Two angles of a triangle are 20° and 125°. What is the third angle? (a) 160° (b) 35° (c) 55° (d) 145°
34. 34.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 80° (b) 135° (c) 100° (d) 145°
35. 35.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 285° (b) 15° (c) 75° (d) 105°
36. 36.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 95° (c) 85° (d) 265°
37. 37.Two angles of a triangle are 20° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 160° (c) 65° (d) 115°
38. 38.Two angles of a triangle are 65° and 75°. What is the third angle? (a) 140° (b) 105° (c) 40° (d) 115°
39. 39.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 140° (b) 71° (c) 70° (d) 110°
40. 40.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) 70° (d) 250°

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