Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 681 · 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 30°. What is each of the other two angles? (a) 30° (b) 75° (c) 60° (d) 150°
2. 2.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 115° (b) 135° (c) 110° (d) 70°
3. 3.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 45° (c) 135° (d) 155°
4. 4.Two angles of a triangle are 35° and 50°. What is the exterior angle at the third corner? (a) 145° (b) 95° (c) 85° (d) 130°
5. 5.Two angles of a triangle are 55° and 85°. What is the third angle? (a) 140° (b) 40° (c) 125° (d) 95°
6. 6.Two angles of a triangle are 60° and 85°. What is the third angle? (a) 35° (b) 120° (c) 145° (d) 95°
7. 7.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 20° (c) 110° (d) 70°
8. 8.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 10° (b) 170° (c) 11° (d) 190°
9. 9.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 80° (c) 20° (d) 160°
10. 10.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 81° (b) 160° (c) 100° (d) 80°
11. 11.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 25° (c) 65° (d) 130°
12. 12.Two angles of a triangle are 45° and 35°. What is the third angle? (a) 80° (b) 135° (c) 100° (d) 145°
13. 13.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 125° (b) 105° (c) 55° (d) 130°
14. 14.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) 30° (d) 40°
15. 15.Two angles of a triangle are 65° and 75°. What is the third angle? (a) 140° (b) 40° (c) 115° (d) 105°
16. 16.Two angles of a triangle are 25° and 145°. What is the third angle? (a) 155° (b) 10° (c) 35° (d) 170°
17. 17.Two angles of a triangle are 45° and 95°. What is the third angle? (a) 40° (b) 140° (c) 85° (d) 135°
18. 18.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 25° (b) 35° (c) 50° (d) 130°
19. 19.Two angles of a triangle are 80° and 55°. What is the third angle? (a) 45° (b) 135° (c) 125° (d) 100°
20. 20.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 85° (c) 86° (d) 170°
21. 21.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 115° (b) 230° (c) 65° (d) 50°
22. 22.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 125° (b) 110° (c) 56° (d) 55°
23. 23.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 100° (b) 80° (c) 10° (d) 280°
24. 24.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) 325° (c) 145° (d) 35°
25. 25.Two angles of a triangle are 75° and 85°. What is the third angle? (a) 160° (b) 20° (c) 105° (d) 95°
26. 26.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) 140° (d) 40°
27. 27.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°
28. 28.Two angles of a triangle are 50° and 50°. What is the exterior angle at the third corner? (a) 100° (b) 260° (c) 130° (d) 80°
29. 29.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 136° (b) 135° (c) 315° (d) 45°
30. 30.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 110° (c) 70° (d) 35°
31. 31.Two angles of a triangle are 65° and 60°. What is the third angle? (a) 125° (b) 115° (c) 55° (d) 120°
32. 32.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 35° (c) 110° (d) 145°
33. 33.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 40° (c) 140° (d) 100°
34. 34.Two angles of a triangle are 40° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 35° (c) 140° (d) 145°
35. 35.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 70° (b) 20° (c) 110° (d) 55°
36. 36.Two angles of a triangle are 25° and 95°. What is the third angle? (a) 60° (b) 155° (c) 85° (d) 120°
37. 37.Two angles of a triangle are 20° and 130°. What is the third angle? (a) 50° (b) 160° (c) 150° (d) 30°
38. 38.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 35° (b) 215° (c) 145° (d) 70°
39. 39.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 140° (c) 40° (d) 50°
40. 40.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 130° (b) 50° (c) 80° (d) 260°

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