Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 740 · 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 50° and 95°. What is the exterior angle at the third corner? (a) 130° (b) 35° (c) 85° (d) 145°
2. 2.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 115° (b) 65° (c) 130° (d) 66°
3. 3.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 115° (c) 65° (d) 100°
4. 4.Two angles of a triangle are 65° and 35°. What is the third angle? (a) 80° (b) 145° (c) 115° (d) 100°
5. 5.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 155° (b) 205° (c) 26° (d) 25°
6. 6.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 25° (b) 130° (c) 50° (d) 35°
7. 7.Two angles of a triangle are 20° and 100°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 80° (d) 160°
8. 8.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) 40° (d) 30°
9. 9.Two angles of a triangle are 35° and 80°. What is the third angle? (a) 65° (b) 100° (c) 115° (d) 145°
10. 10.Two angles of a triangle are 25° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 65° (c) 155° (d) 115°
11. 11.Two angles of a triangle are 70° and 25°. What is the third angle? (a) 95° (b) 110° (c) 155° (d) 85°
12. 12.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 20° (b) 320° (c) 140° (d) 160°
13. 13.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°
14. 14.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 130° (c) 80° (d) 50°
15. 15.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°
16. 16.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 295° (b) 115° (c) 25° (d) 65°
17. 17.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 15° (c) 150° (d) 30°
18. 18.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 100° (b) 280° (c) 140° (d) 40°
19. 19.Two angles of a triangle are 30° and 65°. What is the third angle? (a) 150° (b) 85° (c) 95° (d) 115°
20. 20.Two angles of a triangle are 55° and 40°. What is the third angle? (a) 125° (b) 95° (c) 140° (d) 85°
21. 21.Two angles of a triangle are 80° and 85°. What is the third angle? (a) 165° (b) 15° (c) 100° (d) 95°
22. 22.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 150° (c) 75° (d) 30°
23. 23.Two angles of a triangle are 70° and 70°. What is the exterior angle at the third corner? (a) 40° (b) 110° (c) 220° (d) 140°
24. 24.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 145° (b) 155° (c) 120° (d) 60°
25. 25.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 60° (c) 61° (d) 120°
26. 26.Two angles of a triangle are 35° and 50°. What is the exterior angle at the third corner? (a) 95° (b) 145° (c) 130° (d) 85°
27. 27.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 320° (b) 50° (c) 40° (d) 140°
28. 28.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) 110° (d) 70°
29. 29.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 100° (b) 35° (c) 115° (d) 145°
30. 30.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 260° (b) 130° (c) 50° (d) 80°
31. 31.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 115° (c) 25° (d) 50°
32. 32.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 105° (b) 30° (c) 210° (d) 75°
33. 33.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 170° (c) 85° (d) 95°
34. 34.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 25° (c) 130° (d) 65°
35. 35.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 25° (b) 155° (c) 130° (d) 310°
36. 36.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 60° (b) 145° (c) 155° (d) 120°
37. 37.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 80° (b) 10° (c) 100° (d) 280°
38. 38.Two angles of a triangle are 45° and 65°. What is the exterior angle at the third corner? (a) 70° (b) 115° (c) 110° (d) 135°
39. 39.Two angles of a triangle are 35° and 105°. What is the third angle? (a) 75° (b) 140° (c) 40° (d) 145°
40. 40.Two angles of a triangle are 25° and 40°. What is the third angle? (a) 155° (b) 140° (c) 65° (d) 115°

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