Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 754 · 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 30° and 40°. What is the exterior angle at the third corner? (a) 110° (b) 140° (c) 70° (d) 150°
2. 2.Two angles of a triangle are 35° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 45° (c) 145° (d) 135°
3. 3.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 110° (b) 140° (c) 71° (d) 70°
4. 4.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 40° (c) 70° (d) 50°
5. 5.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) 125° (d) 55°
6. 6.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 130° (c) 155° (d) 25°
7. 7.Two angles of a triangle are 75° and 60°. What is the third angle? (a) 105° (b) 120° (c) 45° (d) 135°
8. 8.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 35° (c) 55° (d) 110°
9. 9.Two angles of a triangle are 55° and 110°. What is the third angle? (a) 125° (b) 70° (c) 15° (d) 165°
10. 10.Two angles of a triangle are 40° and 95°. What is the third angle? (a) 140° (b) 45° (c) 85° (d) 135°
11. 11.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 265° (c) 86° (d) 85°
12. 12.Two angles of a triangle are 80° and 70°. What is the third angle? (a) 110° (b) 100° (c) 150° (d) 30°
13. 13.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 56° (b) 55° (c) 125° (d) 235°
14. 14.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 125° (c) 35° (d) 70°
15. 15.Two angles of a triangle are 70° and 80°. What is the third angle? (a) 110° (b) 150° (c) 100° (d) 30°
16. 16.Two angles of a triangle are 45° and 45°. What is the third angle? (a) 270° (b) 91° (c) 90° (d) 135°
17. 17.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 95° (b) 130° (c) 145° (d) 85°
18. 18.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 50° (c) 65° (d) 40°
19. 19.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 145° (b) 36° (c) 35° (d) 70°
20. 20.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 40° (c) 20° (d) 30°
21. 21.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 65° (b) 115° (c) 66° (d) 245°
22. 22.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 110° (b) 140° (c) 70° (d) 250°
23. 23.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) 70° (c) 20° (d) 160°
24. 24.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 45° (c) 46° (d) 55°
25. 25.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 25° (c) 65° (d) 115°
26. 26.Two angles of a triangle are 60° and 70°. What is the third angle? (a) 120° (b) 130° (c) 110° (d) 50°
27. 27.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 80° (c) 40° (d) 50°
28. 28.Two angles of a triangle are 65° and 85°. What is the third angle? (a) 30° (b) 150° (c) 95° (d) 115°
29. 29.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) 35° (c) 145° (d) 36°
30. 30.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 85° (b) 10° (c) 95° (d) 190°
31. 31.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 160° (b) 140° (c) 20° (d) 320°
32. 32.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 50° (b) 150° (c) 20° (d) 160°
33. 33.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 110° (b) 250° (c) 70° (d) 71°
34. 34.Two angles of a triangle are 20° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 55° (c) 125° (d) 160°
35. 35.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 160° (b) 20° (c) 40° (d) 21°
36. 36.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) 315° (c) 135° (d) 45°
37. 37.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 300° (b) 120° (c) 150° (d) 30°
38. 38.Two angles of a triangle are 20° and 130°. What is the exterior angle at the third corner? (a) 30° (b) 160° (c) 150° (d) 50°
39. 39.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 45° (c) 135° (d) 91°
40. 40.Two angles of a triangle are 20° and 20°. What is the exterior angle at the third corner? (a) 140° (b) 40° (c) 320° (d) 160°

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