Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 152 · 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 90°. What is each of the other two angles? (a) 90° (b) 46° (c) 55° (d) 45°
2. 2.Two angles of a triangle are 50° and 65°. What is the third angle? (a) 245° (b) 65° (c) 115° (d) 130°
3. 3.Two angles of a triangle are 35° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 145° (c) 115° (d) 65°
4. 4.Two angles of a triangle are 30° and 50°. What is the third angle? (a) 130° (b) 150° (c) 100° (d) 80°
5. 5.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 100° (c) 145° (d) 35°
6. 6.Two angles of a triangle are 20° and 85°. What is the third angle? (a) 75° (b) 160° (c) 95° (d) 105°
7. 7.Two angles of a triangle are 40° and 115°. What is the third angle? (a) 140° (b) 25° (c) 65° (d) 155°
8. 8.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 105° (b) 145° (c) 110° (d) 75°
9. 9.Two angles of a triangle are 65° and 105°. What is the third angle? (a) 115° (b) 170° (c) 75° (d) 10°
10. 10.Two angles of a triangle are 75° and 40°. What is the exterior angle at the third corner? (a) 115° (b) 140° (c) 105° (d) 65°
11. 11.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) 125° (d) 55°
12. 12.Two angles of a triangle are 55° and 75°. What is the third angle? (a) 130° (b) 50° (c) 125° (d) 105°
13. 13.Two angles of a triangle are 30° and 85°. What is the exterior angle at the third corner? (a) 115° (b) 150° (c) 95° (d) 65°
14. 14.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 60° (b) 155° (c) 145° (d) 120°
15. 15.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) 260° (d) 130°
16. 16.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 140° (b) 320° (c) 20° (d) 160°
17. 17.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 120° (b) 30° (c) 40° (d) 60°
18. 18.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 100° (c) 80° (d) 105°
19. 19.Two angles of a triangle are 20° and 60°. What is the exterior angle at the third corner? (a) 100° (b) 120° (c) 160° (d) 80°
20. 20.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 195° (b) 16° (c) 165° (d) 15°
21. 21.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 20° (c) 70° (d) 80°
22. 22.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 26° (b) 155° (c) 25° (d) 50°
23. 23.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 30° (c) 40° (d) 20°
24. 24.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 215° (b) 36° (c) 145° (d) 35°
25. 25.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 51° (b) 100° (c) 50° (d) 130°
26. 26.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 10° (c) 20° (d) 80°
27. 27.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 140° (b) 40° (c) 41° (d) 80°
28. 28.Two angles of a triangle are 75° and 55°. What is the third angle? (a) 130° (b) 125° (c) 105° (d) 50°
29. 29.Two angles of a triangle are 40° and 90°. What is the third angle? (a) 140° (b) 90° (c) 130° (d) 50°
30. 30.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 150° (b) 210° (c) 105° (d) 30°
31. 31.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 230° (b) 130° (c) 50° (d) 51°
32. 32.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 30° (c) 60° (d) 120°
33. 33.Two angles of a triangle are 70° and 80°. What is the exterior angle at the third corner? (a) 30° (b) 110° (c) 100° (d) 150°
34. 34.Two angles of a triangle are 20° and 45°. What is the third angle? (a) 135° (b) 65° (c) 115° (d) 160°
35. 35.Two angles of a triangle are 35° and 25°. What is the third angle? (a) 60° (b) 155° (c) 120° (d) 145°
36. 36.Two angles of a triangle are 40° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 270° (c) 140° (d) 90°
37. 37.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 170° (c) 95° (d) 86°
38. 38.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 140° (b) 105° (c) 40° (d) 115°
39. 39.Two angles of a triangle are 20° and 125°. What is the third angle? (a) 145° (b) 55° (c) 160° (d) 35°
40. 40.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 130° (c) 50° (d) 40°

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