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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 233 · 40 questions
TalentJR

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.

NameDateTime takenScore ___ / 40
  1. 1.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 30° (c) 60° (d) 120°
  2. 2.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°
  3. 3.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) 170° (d) 86°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 50° (b) 65° (c) 230° (d) 115°
  5. 5.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 15° (b) 40° (c) 155° (d) 165°
  6. 6.Two angles of a triangle are 20° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 75° (c) 105° (d) 160°
  7. 7.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 15° (c) 105° (d) 30°
  8. 8.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°
  9. 9.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 25° (b) 65° (c) 155° (d) 335°
  10. 10.Two angles of a triangle are 40° and 110°. What is the exterior angle at the third corner? (a) 30° (b) 70° (c) 150° (d) 140°
  11. 11.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 125° (c) 70° (d) 55°
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 45° (b) 90° (c) 135° (d) 46°
  13. 13.Two angles of a triangle are 70° and 100°. What is the third angle? (a) 170° (b) 110° (c) 80° (d) 10°
  14. 14.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 75° (b) 135° (c) 105° (d) 120°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 45° (b) 135° (c) 270° (d) 90°
  16. 16.Two angles of a triangle are 50° and 80°. What is the third angle? (a) 130° (b) 230° (c) 50° (d) 100°
  17. 17.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 85° (c) 10° (d) 5°
  18. 18.Two angles of a triangle are 75° and 65°. What is the exterior angle at the third corner? (a) 40° (b) 115° (c) 140° (d) 105°
  19. 19.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 135° (b) 70° (c) 115° (d) 110°
  20. 20.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 125° (b) 55° (c) 145° (d) 160°
  21. 21.Two angles of a triangle are 50° and 50°. What is the third angle? (a) 100° (b) 260° (c) 130° (d) 80°
  22. 22.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 20° (c) 40° (d) 30°
  23. 23.Two angles of a triangle are 20° and 20°. What is the third angle? (a) 160° (b) 140° (c) 320° (d) 40°
  24. 24.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 100° (b) 155° (c) 80° (d) 105°
  25. 25.Two angles of a triangle are 20° and 135°. What is the third angle? (a) 25° (b) 160° (c) 45° (d) 155°
  26. 26.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 30° (c) 150° (d) 60°
  27. 27.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 70° (b) 290° (c) 110° (d) 20°
  28. 28.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 45° (b) 100° (c) 125° (d) 135°
  29. 29.Two angles of a triangle are 30° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 80° (c) 150° (d) 100°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 51° (b) 50° (c) 130° (d) 100°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 80° (c) 100° (d) 50°
  32. 32.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) 45° (c) 225° (d) 46°
  33. 33.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 120° (b) 145° (c) 85° (d) 95°
  34. 34.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 310° (b) 50° (c) 40° (d) 130°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 31° (b) 30° (c) 150° (d) 60°
  36. 36.Two angles of a triangle are 25° and 120°. What is the third angle? (a) 155° (b) 60° (c) 145° (d) 35°
  37. 37.Two angles of a triangle are 65° and 20°. What is the third angle? (a) 85° (b) 160° (c) 115° (d) 95°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 250° (b) 70° (c) 125° (d) 55°
  39. 39.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 80° (b) 81° (c) 100° (d) 260°
  40. 40.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 10° (c) 160° (d) 11°

Answer key

  1. 60°
  2. 75°
  3. 85°
  4. 115°
  5. 15°
  6. 75°
  7. 30°
  8. 70°
  9. 155°
  10. 150°
  11. 70°
  12. 45°
  13. 10°
  14. 75°
  15. 135°
  16. 50°
  17. 10°
  18. 140°
  19. 70°
  20. 55°
  21. 80°
  22. 20°
  23. 140°
  24. 100°
  25. 25°
  26. 120°
  27. 110°
  28. 135°
  29. 80°
  30. 50°
  31. 40°
  32. 45°
  33. 95°
  34. 130°
  35. 30°
  36. 35°
  37. 95°
  38. 125°
  39. 80°
  40. 10°

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