Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 331 · 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 45° and 120°. What is the third angle? (a) 15° (b) 135° (c) 165° (d) 60°
2. 2.Two angles of a triangle are 25° and 25°. What is the third angle? (a) 310° (b) 50° (c) 130° (d) 155°
3. 3.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 120° (c) 150° (d) 60°
4. 4.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 10° (b) 20° (c) 11° (d) 170°
5. 5.Two angles of a triangle are 65° and 40°. What is the third angle? (a) 105° (b) 115° (c) 75° (d) 140°
6. 6.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 20° (b) 140° (c) 30° (d) 40°
7. 7.Two angles of a triangle are 55° and 25°. What is the exterior angle at the third corner? (a) 100° (b) 125° (c) 155° (d) 80°
8. 8.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 95° (c) 5° (d) 10°
9. 9.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 60° (c) 120° (d) 61°
10. 10.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 65° (b) 115° (c) 230° (d) 50°
11. 11.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 85° (c) 170° (d) 95°
12. 12.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 135° (b) 46° (c) 45° (d) 225°
13. 13.Two angles of a triangle are 45° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 135° (c) 140° (d) 40°
14. 14.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 55° (c) 105° (d) 125°
15. 15.Two angles of a triangle are 65° and 65°. What is the third angle? (a) 130° (b) 230° (c) 115° (d) 50°
16. 16.Two angles of a triangle are 45° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 135° (c) 145° (d) 35°
17. 17.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 15° (c) 150° (d) 25°
18. 18.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 110° (c) 45° (d) 35°
19. 19.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 110° (b) 130° (c) 160° (d) 70°
20. 20.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 95° (c) 85° (d) 86°
21. 21.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 105° (c) 30° (d) 75°
22. 22.Two angles of a triangle are 45° and 45°. What is the exterior angle at the third corner? (a) 91° (b) 135° (c) 90° (d) 270°
23. 23.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 70° (c) 140° (d) 50°
24. 24.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 310° (b) 155° (c) 25° (d) 130°
25. 25.Two angles of a triangle are 30° and 120°. What is the third angle? (a) 150° (b) 210° (c) 30° (d) 60°
26. 26.Two angles of a triangle are 20° and 150°. What is the third angle? (a) 30° (b) 160° (c) 10° (d) 170°
27. 27.Two angles of a triangle are 55° and 30°. What is the exterior angle at the third corner? (a) 95° (b) 150° (c) 85° (d) 125°
28. 28.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 125° (c) 70° (d) 55°
29. 29.Two angles of a triangle are 55° and 25°. What is the third angle? (a) 80° (b) 100° (c) 155° (d) 125°
30. 30.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 130° (c) 25° (d) 50°
31. 31.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 125° (b) 120° (c) 115° (d) 60°
32. 32.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) 205° (c) 155° (d) 25°
33. 33.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 155° (b) 25° (c) 100° (d) 105°
34. 34.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 10° (c) 50° (d) 80°
35. 35.Two angles of a triangle are 65° and 55°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 125° (d) 115°
36. 36.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 20° (c) 80° (d) 160°
37. 37.Two angles of a triangle are 30° and 90°. What is the third angle? (a) 60° (b) 150° (c) 90° (d) 120°
38. 38.Two angles of a triangle are 30° and 95°. What is the exterior angle at the third corner? (a) 150° (b) 125° (c) 85° (d) 55°
39. 39.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 100° (c) 140° (d) 280°
40. 40.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 35° (b) 145° (c) 100° (d) 115°

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