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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 6 · 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.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 60° (c) 120° (d) 160°
  2. 2.Two angles of a triangle are 60° and 70°. What is the third angle? (a) 130° (b) 120° (c) 50° (d) 110°
  3. 3.Two angles of a triangle are 30° and 30°. What is the exterior angle at the third corner? (a) 60° (b) 150° (c) 300° (d) 120°
  4. 4.Two angles of a triangle are 20° and 85°. What is the third angle? (a) 160° (b) 95° (c) 75° (d) 105°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 20° (c) 160° (d) 10°
  6. 6.Two angles of a triangle are 25° and 25°. What is the third angle? (a) 310° (b) 50° (c) 155° (d) 130°
  7. 7.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°
  8. 8.Two angles of a triangle are 70° and 80°. What is the exterior angle at the third corner? (a) 150° (b) 110° (c) 30° (d) 100°
  9. 9.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 70° (b) 340° (c) 20° (d) 160°
  10. 10.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 60° (b) 100° (c) 140° (d) 120°
  11. 11.Two angles of a triangle are 45° and 40°. What is the third angle? (a) 95° (b) 140° (c) 135° (d) 85°
  12. 12.Two angles of a triangle are 40° and 105°. What is the third angle? (a) 140° (b) 75° (c) 145° (d) 35°
  13. 13.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 40° (b) 140° (c) 105° (d) 115°
  14. 14.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 160° (d) 125°
  15. 15.Two angles of a triangle are 30° and 100°. What is the exterior angle at the third corner? (a) 130° (b) 80° (c) 50° (d) 150°
  16. 16.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 110° (c) 130° (d) 70°
  17. 17.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 140° (c) 50° (d) 40°
  18. 18.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 35° (b) 55° (c) 145° (d) 325°
  19. 19.Two angles of a triangle are 20° and 30°. What is the exterior angle at the third corner? (a) 130° (b) 150° (c) 50° (d) 160°
  20. 20.Two angles of a triangle are 70° and 85°. What is the third angle? (a) 95° (b) 25° (c) 155° (d) 110°
  21. 21.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) 60° (d) 150°
  22. 22.Two angles of a triangle are 35° and 125°. What is the third angle? (a) 55° (b) 160° (c) 20° (d) 145°
  23. 23.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) 30° (d) 40°
  24. 24.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) 160° (d) 20°
  25. 25.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 85° (c) 95° (d) 86°
  26. 26.Two angles of a triangle are 75° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 115° (c) 65° (d) 105°
  27. 27.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 130° (c) 40° (d) 65°
  28. 28.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 35° (c) 110° (d) 70°
  29. 29.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) 85° (c) 86° (d) 95°
  30. 30.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 95° (b) 85° (c) 145° (d) 130°
  31. 31.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 75° (b) 135° (c) 105° (d) 120°
  32. 32.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 140° (b) 220° (c) 40° (d) 41°
  33. 33.Two angles of a triangle are 80° and 50°. What is the third angle? (a) 100° (b) 50° (c) 130° (d) 230°
  34. 34.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 20° (c) 70° (d) 40°
  35. 35.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 30° (c) 15° (d) 105°
  36. 36.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 30° (c) 120° (d) 60°
  37. 37.Two angles of a triangle are 40° and 120°. What is the third angle? (a) 140° (b) 60° (c) 20° (d) 160°
  38. 38.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 25° (c) 65° (d) 155°
  39. 39.Two angles of a triangle are 70° and 60°. What is the third angle? (a) 110° (b) 120° (c) 130° (d) 50°
  40. 40.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 85° (d) 95°

Answer key

  1. 60°
  2. 50°
  3. 60°
  4. 75°
  5. 10°
  6. 130°
  7. 55°
  8. 150°
  9. 160°
  10. 120°
  11. 95°
  12. 35°
  13. 40°
  14. 75°
  15. 130°
  16. 110°
  17. 70°
  18. 145°
  19. 50°
  20. 25°
  21. 30°
  22. 20°
  23. 20°
  24. 20°
  25. 85°
  26. 115°
  27. 65°
  28. 35°
  29. 85°
  30. 95°
  31. 75°
  32. 40°
  33. 50°
  34. 40°
  35. 30°
  36. 120°
  37. 20°
  38. 130°
  39. 50°
  40. 95°

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