Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 611 · 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 80°. What is the exterior angle at the third corner? (a) 125° (b) 135° (c) 100° (d) 55°
2. 2.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 70° (b) 250° (c) 55° (d) 125°
3. 3.Two angles of a triangle are 45° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 130° (c) 50° (d) 135°
4. 4.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 160° (b) 21° (c) 20° (d) 200°
5. 5.Two angles of a triangle are 30° and 60°. What is the third angle? (a) 150° (b) 270° (c) 90° (d) 120°
6. 6.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 105° (b) 140° (c) 115° (d) 40°
7. 7.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 140° (c) 70° (d) 40°
8. 8.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 90° (b) 115° (c) 155° (d) 270°
9. 9.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 56° (b) 125° (c) 55° (d) 110°
10. 10.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 50° (b) 230° (c) 130° (d) 51°
11. 11.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 46° (c) 45° (d) 90°
12. 12.Two angles of a triangle are 45° and 75°. What is the third angle? (a) 60° (b) 105° (c) 135° (d) 120°
13. 13.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 30° (c) 60° (d) 120°
14. 14.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 215° (b) 36° (c) 35° (d) 145°
15. 15.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 110° (b) 135° (c) 70° (d) 115°
16. 16.Two angles of a triangle are 50° and 25°. What is the third angle? (a) 75° (b) 105° (c) 130° (d) 155°
17. 17.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 160° (c) 80° (d) 70°
18. 18.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 50° (c) 130° (d) 25°
19. 19.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 80° (c) 130° (d) 50°
20. 20.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 135° (b) 45° (c) 315° (d) 136°
21. 21.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 250° (b) 70° (c) 140° (d) 110°
22. 22.Two angles of a triangle are 50° and 95°. What is the exterior angle at the third corner? (a) 35° (b) 130° (c) 85° (d) 145°
23. 23.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 170° (b) 10° (c) 20° (d) 11°
24. 24.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 10° (c) 5° (d) 95°
25. 25.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 75° (b) 15° (c) 285° (d) 105°
26. 26.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 150° (c) 120° (d) 30°
27. 27.Two angles of a triangle are 50° and 90°. What is the third angle? (a) 140° (b) 90° (c) 130° (d) 40°
28. 28.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°
29. 29.Two angles of a triangle are 70° and 20°. What is the third angle? (a) 110° (b) 90° (c) 270° (d) 160°
30. 30.Two angles of a triangle are 40° and 85°. What is the exterior angle at the third corner? (a) 55° (b) 95° (c) 140° (d) 125°
31. 31.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 40° (c) 50° (d) 100°
32. 32.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 160° (b) 20° (c) 70° (d) 340°
33. 33.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) 25° (d) 155°
34. 34.Two angles of a triangle are 65° and 55°. What is the exterior angle at the third corner? (a) 115° (b) 60° (c) 120° (d) 125°
35. 35.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 65° (c) 50° (d) 40°
36. 36.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 120° (c) 61° (d) 60°
37. 37.Two angles of a triangle are 60° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 115° (c) 65° (d) 120°
38. 38.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 190° (b) 170° (c) 10° (d) 11°
39. 39.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 120° (b) 115° (c) 125° (d) 60°
40. 40.Two angles of a triangle are 65° and 20°. What is the third angle? (a) 160° (b) 85° (c) 95° (d) 115°

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