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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 947 · 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 75° each. What is the third angle? (a) 75° (b) 30° (c) 105° (d) 15°
  2. 2.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 105° (c) 80° (d) 100°
  3. 3.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°
  4. 4.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°
  5. 5.Two angles of a triangle are 20° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 120° (c) 160° (d) 60°
  6. 6.Two angles of a triangle are 45° and 20°. What is the third angle? (a) 65° (b) 115° (c) 135° (d) 160°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 40° (c) 140° (d) 20°
  8. 8.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 280° (b) 80° (c) 100° (d) 140°
  9. 9.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 40° (c) 140° (d) 100°
  10. 10.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 120° (b) 60° (c) 300° (d) 30°
  11. 11.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 80° (c) 10° (d) 100°
  12. 12.Two angles of a triangle are 35° and 95°. What is the third angle? (a) 130° (b) 145° (c) 85° (d) 50°
  13. 13.Two angles of a triangle are 60° and 70°. What is the exterior angle at the third corner? (a) 50° (b) 110° (c) 120° (d) 130°
  14. 14.Two angles of a triangle are 30° and 80°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 150° (d) 100°
  15. 15.Two angles of a triangle are 40° and 95°. What is the third angle? (a) 140° (b) 45° (c) 85° (d) 135°
  16. 16.Two angles of a triangle are 35° and 30°. What is the third angle? (a) 65° (b) 145° (c) 150° (d) 115°
  17. 17.Two angles of a triangle are 25° and 100°. What is the third angle? (a) 125° (b) 155° (c) 80° (d) 55°
  18. 18.Two angles of a triangle are 20° and 40°. What is the third angle? (a) 60° (b) 120° (c) 140° (d) 160°
  19. 19.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 70° (b) 45° (c) 135° (d) 155°
  20. 20.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 30° (c) 70° (d) 60°
  21. 21.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 155° (c) 130° (d) 25°
  22. 22.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 135° (b) 75° (c) 150° (d) 30°
  23. 23.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 71° (b) 70° (c) 110° (d) 250°
  24. 24.Two angles of a triangle are 55° and 95°. What is the exterior angle at the third corner? (a) 125° (b) 30° (c) 85° (d) 150°
  25. 25.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 280° (b) 100° (c) 40° (d) 140°
  26. 26.Two angles of a triangle are 70° and 70°. What is the third angle? (a) 140° (b) 40° (c) 220° (d) 110°
  27. 27.Two angles of a triangle are 80° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 125° (c) 100° (d) 55°
  28. 28.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 30° (c) 60° (d) 75°
  29. 29.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 115° (c) 65° (d) 50°
  30. 30.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 35° (c) 70° (d) 45°
  31. 31.Two angles of a triangle are 35° and 120°. What is the third angle? (a) 155° (b) 145° (c) 60° (d) 25°
  32. 32.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 35° (b) 305° (c) 125° (d) 55°
  33. 33.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) 105° (d) 285°
  34. 34.Two angles of a triangle are 60° and 50°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 120° (d) 130°
  35. 35.Two angles of a triangle are 65° and 20°. What is the third angle? (a) 160° (b) 85° (c) 115° (d) 95°
  36. 36.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) 55° (d) 56°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 130° (b) 50° (c) 51° (d) 100°
  38. 38.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 200° (b) 21° (c) 20° (d) 160°
  39. 39.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 140° (b) 80° (c) 100° (d) 120°
  40. 40.Two angles of a triangle are 20° and 105°. What is the third angle? (a) 125° (b) 75° (c) 55° (d) 160°

Answer key

  1. 30°
  2. 100°
  3. 155°
  4. 130°
  5. 120°
  6. 115°
  7. 20°
  8. 100°
  9. 100°
  10. 120°
  11. 50°
  12. 50°
  13. 130°
  14. 110°
  15. 45°
  16. 115°
  17. 55°
  18. 120°
  19. 135°
  20. 60°
  21. 130°
  22. 150°
  23. 70°
  24. 150°
  25. 140°
  26. 40°
  27. 125°
  28. 75°
  29. 50°
  30. 35°
  31. 25°
  32. 125°
  33. 105°
  34. 110°
  35. 95°
  36. 55°
  37. 50°
  38. 20°
  39. 80°
  40. 55°

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