Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 485 · 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. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 235° (b) 55° (c) 56° (d) 125°
2. 2.Two angles of a triangle are 30° and 75°. What is the exterior angle at the third corner? (a) 255° (b) 150° (c) 105° (d) 75°
3. 3.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 55° (b) 35° (c) 325° (d) 145°
4. 4.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 10° (c) 100° (d) 50°
5. 5.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 130° (c) 155° (d) 65°
6. 6.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 35° (c) 55° (d) 70°
7. 7.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 140° (b) 160° (c) 20° (d) 320°
8. 8.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 30° (c) 150° (d) 120°
9. 9.Two angles of a triangle are 65° and 55°. What is the exterior angle at the third corner? (a) 120° (b) 60° (c) 125° (d) 115°
10. 10.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°
11. 11.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 75° (c) 105° (d) 255°
12. 12.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 95° (c) 265° (d) 86°
13. 13.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 80° (c) 40° (d) 130°
14. 14.Two angles of a triangle are 45° and 85°. What is the third angle? (a) 130° (b) 95° (c) 135° (d) 50°
15. 15.Two angles of a triangle are 60° and 105°. What is the third angle? (a) 165° (b) 75° (c) 15° (d) 120°
16. 16.Two angles of a triangle are 55° and 105°. What is the third angle? (a) 160° (b) 125° (c) 75° (d) 20°
17. 17.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 26° (b) 155° (c) 205° (d) 25°
18. 18.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 110° (c) 70° (d) 55°
19. 19.Two angles of a triangle are 50° and 70°. What is the exterior angle at the third corner? (a) 120° (b) 110° (c) 60° (d) 130°
20. 20.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 46° (c) 90° (d) 55°
21. 21.Two angles of a triangle are 40° and 60°. What is the third angle? (a) 80° (b) 140° (c) 120° (d) 100°
22. 22.Two angles of a triangle are 50° and 120°. What is the third angle? (a) 60° (b) 130° (c) 170° (d) 10°
23. 23.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 31° (b) 30° (c) 150° (d) 210°
24. 24.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 45° (b) 46° (c) 90° (d) 135°
25. 25.Two angles of a triangle are 45° and 95°. What is the exterior angle at the third corner? (a) 140° (b) 135° (c) 85° (d) 40°
26. 26.Two angles of a triangle are 25° and 30°. What is the third angle? (a) 150° (b) 155° (c) 125° (d) 55°
27. 27.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 10° (b) 11° (c) 20° (d) 170°
28. 28.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 140° (b) 100° (c) 120° (d) 80°
29. 29.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 25° (c) 150° (d) 15°
30. 30.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 305° (b) 125° (c) 55° (d) 35°
31. 31.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 35° (c) 110° (d) 55°
32. 32.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 100° (b) 260° (c) 81° (d) 80°
33. 33.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 45° (b) 46° (c) 225° (d) 135°
34. 34.Two angles of a triangle are 55° and 60°. What is the exterior angle at the third corner? (a) 65° (b) 125° (c) 115° (d) 120°
35. 35.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 150° (b) 55° (c) 125° (d) 155°
36. 36.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 110° (b) 125° (c) 55° (d) 56°
37. 37.Two angles of a triangle are 20° and 120°. What is the third angle? (a) 60° (b) 140° (c) 160° (d) 40°
38. 38.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 35° (c) 50° (d) 25°
39. 39.Two angles of a triangle are 55° and 40°. What is the third angle? (a) 85° (b) 95° (c) 140° (d) 125°
40. 40.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 10° (c) 20° (d) 100°

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