Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 120 · 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 70°. What is each of the other two angles? (a) 20° (b) 110° (c) 70° (d) 55°
2. 2.Two angles of a triangle are 40° and 30°. What is the exterior angle at the third corner? (a) 140° (b) 70° (c) 150° (d) 110°
3. 3.Two angles of a triangle are 40° and 110°. What is the exterior angle at the third corner? (a) 150° (b) 70° (c) 30° (d) 140°
4. 4.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) 75° (d) 210°
5. 5.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) 65° (d) 25°
6. 6.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) 35° (c) 55° (d) 125°
7. 7.Two angles of a triangle are 40° and 60°. What is the third angle? (a) 140° (b) 120° (c) 80° (d) 100°
8. 8.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 50° (c) 25° (d) 115°
9. 9.Two angles of a triangle are 40° and 115°. What is the third angle? (a) 155° (b) 25° (c) 65° (d) 140°
10. 10.Two angles of a triangle are 35° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 100° (c) 80° (d) 145°
11. 11.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 55° (b) 250° (c) 70° (d) 125°
12. 12.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°
13. 13.Two angles of a triangle are 30° and 20°. What is the third angle? (a) 160° (b) 150° (c) 50° (d) 130°
14. 14.Two angles of a triangle are 35° and 55°. What is the third angle? (a) 90° (b) 145° (c) 270° (d) 125°
15. 15.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 120° (b) 110° (c) 70° (d) 130°
16. 16.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 50° (c) 35° (d) 25°
17. 17.Two angles of a triangle are 25° and 45°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 155° (d) 135°
18. 18.Two angles of a triangle are 40° and 85°. What is the third angle? (a) 140° (b) 125° (c) 95° (d) 55°
19. 19.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 65° (c) 155° (d) 25°
20. 20.Two angles of a triangle are 50° and 95°. What is the third angle? (a) 145° (b) 130° (c) 85° (d) 35°
21. 21.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 75° (c) 150° (d) 60°
22. 22.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 150° (b) 105° (c) 75° (d) 76°
23. 23.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 160° (c) 10° (d) 11°
24. 24.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 85° (b) 190° (c) 10° (d) 95°
25. 25.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 61° (c) 120° (d) 60°
26. 26.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 340° (b) 160° (c) 70° (d) 20°
27. 27.Two angles of a triangle are 75° and 30°. What is the third angle? (a) 105° (b) 75° (c) 150° (d) 255°
28. 28.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 165° (b) 110° (c) 85° (d) 15°
29. 29.Two angles of a triangle are 75° and 45°. What is the exterior angle at the third corner? (a) 105° (b) 135° (c) 60° (d) 120°
30. 30.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 120° (c) 60° (d) 70°
31. 31.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 290° (b) 35° (c) 145° (d) 110°
32. 32.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 130° (c) 75° (d) 155°
33. 33.Two angles of a triangle are 65° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 115° (c) 65° (d) 245°
34. 34.Two angles of a triangle are 20° and 135°. What is the third angle? (a) 45° (b) 25° (c) 155° (d) 160°
35. 35.Two angles of a triangle are 30° and 50°. What is the exterior angle at the third corner? (a) 100° (b) 150° (c) 80° (d) 130°
36. 36.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 120° (b) 60° (c) 140° (d) 160°
37. 37.Two angles of a triangle are 45° and 60°. What is the exterior angle at the third corner? (a) 105° (b) 135° (c) 75° (d) 120°
38. 38.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) 81° (c) 80° (d) 260°
39. 39.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 285° (b) 105° (c) 15° (d) 75°
40. 40.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 115° (b) 130° (c) 66° (d) 65°

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad