Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 257 · 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. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 41° (b) 140° (c) 80° (d) 40°
2. 2.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 320° (b) 20° (c) 140° (d) 160°
3. 3.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 30° (c) 120° (d) 60°
4. 4.Two angles of a triangle are 30° and 20°. What is the third angle? (a) 50° (b) 150° (c) 160° (d) 130°
5. 5.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 140° (c) 100° (d) 50°
6. 6.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 105° (b) 85° (c) 160° (d) 95°
7. 7.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 100° (c) 10° (d) 50°
8. 8.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 80° (c) 10° (d) 20°
9. 9.Two angles of a triangle are 35° and 55°. What is the third angle? (a) 145° (b) 125° (c) 270° (d) 90°
10. 10.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 155° (b) 335° (c) 65° (d) 25°
11. 11.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 140° (b) 100° (c) 120° (d) 40°
12. 12.Two angles of a triangle are 55° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 60° (c) 125° (d) 120°
13. 13.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 130° (c) 25° (d) 35°
14. 14.Two angles of a triangle are 35° and 130°. What is the third angle? (a) 50° (b) 145° (c) 15° (d) 165°
15. 15.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 10° (b) 160° (c) 20° (d) 11°
16. 16.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 230° (b) 50° (c) 65° (d) 115°
17. 17.Two angles of a triangle are 25° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 85° (c) 95° (d) 155°
18. 18.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 100° (c) 105° (d) 75°
19. 19.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 205° (b) 26° (c) 155° (d) 25°
20. 20.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 120° (b) 40° (c) 60° (d) 30°
21. 21.Two angles of a triangle are 30° and 40°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 150° (d) 140°
22. 22.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 95° (c) 85° (d) 170°
23. 23.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 25° (b) 26° (c) 155° (d) 50°
24. 24.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 170° (b) 11° (c) 10° (d) 190°
25. 25.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 60° (c) 30° (d) 75°
26. 26.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 30° (b) 120° (c) 150° (d) 90°
27. 27.Two angles of a triangle are 25° and 25°. What is the exterior angle at the third corner? (a) 130° (b) 155° (c) 310° (d) 50°
28. 28.Two angles of a triangle are 30° and 30°. What is the third angle? (a) 150° (b) 60° (c) 120° (d) 300°
29. 29.Two angles of a triangle are 30° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 105° (c) 75° (d) 150°
30. 30.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 80° (c) 100° (d) 50°
31. 31.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 110° (c) 55° (d) 35°
32. 32.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 20° (b) 40° (c) 30° (d) 140°
33. 33.Two angles of a triangle are 40° and 45°. What is the third angle? (a) 85° (b) 135° (c) 95° (d) 140°
34. 34.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 70° (b) 130° (c) 110° (d) 120°
35. 35.Two angles of a triangle are 35° and 135°. What is the third angle? (a) 10° (b) 45° (c) 170° (d) 145°
36. 36.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 260° (b) 80° (c) 130° (d) 50°
37. 37.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 51° (b) 230° (c) 130° (d) 50°
38. 38.Two angles of a triangle are 30° and 140°. What is the third angle? (a) 150° (b) 40° (c) 170° (d) 10°
39. 39.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 155° (b) 130° (c) 310° (d) 25°
40. 40.Two angles of a triangle are 60° and 55°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 120° (d) 125°

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