Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 182 · 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 35° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 55° (c) 125° (d) 145°
2. 2.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 135° (b) 45° (c) 90° (d) 270°
3. 3.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 150° (b) 30° (c) 115° (d) 95°
4. 4.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 310° (b) 40° (c) 130° (d) 50°
5. 5.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 150° (b) 31° (c) 30° (d) 60°
6. 6.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 30° (c) 60° (d) 75°
7. 7.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 270° (b) 125° (c) 145° (d) 90°
8. 8.Two angles of a triangle are 50° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 260° (c) 80° (d) 100°
9. 9.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 60° (b) 120° (c) 30° (d) 40°
10. 10.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 80° (b) 160° (c) 100° (d) 81°
11. 11.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 21° (b) 20° (c) 40° (d) 160°
12. 12.Two angles of a triangle are 30° and 110°. What is the exterior angle at the third corner? (a) 150° (b) 70° (c) 140° (d) 40°
13. 13.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 35° (c) 110° (d) 55°
14. 14.Two angles of a triangle are 30° and 105°. What is the exterior angle at the third corner? (a) 135° (b) 75° (c) 150° (d) 45°
15. 15.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 55° (b) 20° (c) 110° (d) 70°
16. 16.Two angles of a triangle are 30° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 80° (c) 150° (d) 100°
17. 17.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 80° (b) 20° (c) 100° (d) 200°
18. 18.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 70° (c) 35° (d) 125°
19. 19.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 80° (c) 70° (d) 20°
20. 20.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 65° (c) 50° (d) 25°
21. 21.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 100° (b) 80° (c) 140° (d) 120°
22. 22.Two angles of a triangle are 30° and 80°. What is the third angle? (a) 110° (b) 100° (c) 70° (d) 150°
23. 23.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 30° (c) 61° (d) 60°
24. 24.Two angles of a triangle are 20° and 30°. What is the third angle? (a) 50° (b) 130° (c) 160° (d) 150°
25. 25.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 80° (b) 100° (c) 135° (d) 125°
26. 26.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 35° (b) 100° (c) 145° (d) 115°
27. 27.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) 25° (c) 155° (d) 335°
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) 55° (c) 305° (d) 125°
29. 29.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 45° (c) 135° (d) 90°
30. 30.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°
31. 31.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 85° (b) 105° (c) 160° (d) 95°
32. 32.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 60° (b) 150° (c) 30° (d) 330°
33. 33.Two angles of a triangle are 40° and 115°. What is the third angle? (a) 155° (b) 140° (c) 65° (d) 25°
34. 34.Two angles of a triangle are 75° and 65°. What is the exterior angle at the third corner? (a) 40° (b) 105° (c) 140° (d) 115°
35. 35.Two angles of a triangle are 35° and 65°. What is the third angle? (a) 100° (b) 80° (c) 145° (d) 115°
36. 36.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 110° (b) 220° (c) 40° (d) 70°
37. 37.Two angles of a triangle are 50° and 80°. What is the third angle? (a) 230° (b) 130° (c) 100° (d) 50°
38. 38.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 110° (c) 70° (d) 20°
39. 39.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°
40. 40.Two angles of a triangle are 25° and 130°. What is the third angle? (a) 155° (b) 25° (c) 50° (d) 205°

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