Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 454 · 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 40°. What is each of the other two angles? (a) 40° (b) 140° (c) 50° (d) 70°
2. 2.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 10° (b) 190° (c) 95° (d) 85°
3. 3.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 220° (b) 40° (c) 70° (d) 110°
4. 4.Two angles of a triangle are 35° and 75°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 105° (d) 145°
5. 5.Two angles of a triangle are 55° and 70°. What is the exterior angle at the third corner? (a) 125° (b) 55° (c) 110° (d) 235°
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) 40° (b) 220° (c) 140° (d) 41°
7. 7.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 55° (c) 45° (d) 46°
8. 8.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 130° (c) 25° (d) 65°
9. 9.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 25° (b) 155° (c) 105° (d) 100°
10. 10.Two angles of a triangle are 60° and 75°. What is the third angle? (a) 135° (b) 45° (c) 105° (d) 120°
11. 11.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) 125° (c) 55° (d) 56°
12. 12.Two angles of a triangle are 75° and 45°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 135° (d) 105°
13. 13.Two angles of a triangle are 75° and 75°. What is the exterior angle at the third corner? (a) 30° (b) 150° (c) 210° (d) 105°
14. 14.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 70° (b) 145° (c) 105° (d) 110°
15. 15.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 95° (c) 10° (d) 85°
16. 16.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 130° (c) 25° (d) 50°
17. 17.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 130° (b) 150° (c) 80° (d) 100°
18. 18.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 100° (c) 120° (d) 60°
19. 19.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 135° (b) 100° (c) 125° (d) 45°
20. 20.Two angles of a triangle are 35° and 70°. What is the third angle? (a) 110° (b) 145° (c) 75° (d) 105°
21. 21.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 155° (b) 26° (c) 50° (d) 25°
22. 22.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 70° (c) 60° (d) 30°
23. 23.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 270° (b) 90° (c) 135° (d) 45°
24. 24.Two angles of a triangle are 80° and 80°. What is the third angle? (a) 100° (b) 160° (c) 20° (d) 200°
25. 25.Two angles of a triangle are 65° and 90°. What is the third angle? (a) 90° (b) 155° (c) 25° (d) 115°
26. 26.Two angles of a triangle are 20° and 45°. What is the exterior angle at the third corner? (a) 115° (b) 160° (c) 135° (d) 65°
27. 27.Two angles of a triangle are 40° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 95° (c) 140° (d) 85°
28. 28.Two angles of a triangle are 50° and 75°. What is the third angle? (a) 105° (b) 55° (c) 130° (d) 125°
29. 29.Two angles of a triangle are 70° and 45°. What is the third angle? (a) 115° (b) 135° (c) 65° (d) 110°
30. 30.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 110° (b) 90° (c) 160° (d) 270°
31. 31.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 66° (b) 115° (c) 245° (d) 65°
32. 32.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 140° (b) 40° (c) 280° (d) 100°
33. 33.Two angles of a triangle are 20° and 95°. What is the third angle? (a) 115° (b) 160° (c) 65° (d) 85°
34. 34.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 35° (c) 55° (d) 110°
35. 35.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 65° (c) 50° (d) 115°
36. 36.Two angles of a triangle are 20° and 110°. What is the exterior angle at the third corner? (a) 130° (b) 50° (c) 70° (d) 160°
37. 37.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°
38. 38.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 105° (c) 145° (d) 75°
39. 39.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°
40. 40.Two angles of a triangle are 65° and 50°. What is the third angle? (a) 245° (b) 130° (c) 65° (d) 115°

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