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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 286 · 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 70° and 60°. What is the exterior angle at the third corner? (a) 50° (b) 120° (c) 110° (d) 130°
  2. 2.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 31° (b) 60° (c) 30° (d) 150°
  3. 3.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 125° (b) 75° (c) 105° (d) 160°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 55° (b) 70° (c) 125° (d) 250°
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 60° (b) 240° (c) 121° (d) 120°
  6. 6.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 155° (d) 145°
  7. 7.Two angles of a triangle are 25° and 75°. What is the exterior angle at the third corner? (a) 80° (b) 105° (c) 155° (d) 100°
  8. 8.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 95° (b) 85° (c) 150° (d) 115°
  9. 9.Two angles of a triangle are 70° and 70°. What is the exterior angle at the third corner? (a) 140° (b) 220° (c) 110° (d) 40°
  10. 10.Two angles of a triangle are 25° and 40°. What is the third angle? (a) 65° (b) 115° (c) 140° (d) 155°
  11. 11.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 55° (b) 125° (c) 155° (d) 150°
  12. 12.Two angles of a triangle are 55° and 30°. What is the third angle? (a) 150° (b) 85° (c) 95° (d) 125°
  13. 13.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 30° (c) 60° (d) 150°
  14. 14.Two angles of a triangle are 70° and 20°. What is the third angle? (a) 110° (b) 270° (c) 90° (d) 160°
  15. 15.Two angles of a triangle are 70° and 70°. What is the third angle? (a) 40° (b) 220° (c) 110° (d) 140°
  16. 16.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 105° (b) 85° (c) 160° (d) 95°
  17. 17.Two angles of a triangle are 50° and 120°. What is the third angle? (a) 130° (b) 170° (c) 10° (d) 60°
  18. 18.Two angles of a triangle are 55° and 80°. What is the exterior angle at the third corner? (a) 125° (b) 100° (c) 135° (d) 45°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 70° (b) 20° (c) 110° (d) 55°
  20. 20.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 25° (c) 130° (d) 65°
  21. 21.Two angles of a triangle are 70° and 60°. What is the third angle? (a) 50° (b) 120° (c) 130° (d) 110°
  22. 22.Two angles of a triangle are 40° and 90°. What is the third angle? (a) 140° (b) 130° (c) 50° (d) 90°
  23. 23.Two angles of a triangle are 55° and 60°. What is the third angle? (a) 125° (b) 120° (c) 115° (d) 65°
  24. 24.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 125° (b) 60° (c) 115° (d) 120°
  25. 25.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 60° (c) 61° (d) 120°
  26. 26.Two angles of a triangle are 60° and 20°. What is the exterior angle at the third corner? (a) 120° (b) 160° (c) 80° (d) 100°
  27. 27.Two angles of a triangle are 30° and 50°. What is the third angle? (a) 130° (b) 80° (c) 100° (d) 150°
  28. 28.Two angles of a triangle are 30° and 125°. What is the third angle? (a) 55° (b) 25° (c) 155° (d) 150°
  29. 29.Two angles of a triangle are 30° and 35°. What is the third angle? (a) 150° (b) 145° (c) 115° (d) 65°
  30. 30.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 240° (b) 61° (c) 120° (d) 60°
  31. 31.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 320° (b) 40° (c) 50° (d) 140°
  32. 32.Two angles of a triangle are 75° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 30° (c) 210° (d) 150°
  33. 33.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 70° (c) 250° (d) 110°
  34. 34.Two angles of a triangle are 20° and 140°. What is the third angle? (a) 160° (b) 20° (c) 200° (d) 40°
  35. 35.Two angles of a triangle are 70° and 100°. What is the third angle? (a) 10° (b) 80° (c) 170° (d) 110°
  36. 36.Two angles of a triangle are 65° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 125° (c) 115° (d) 55°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 160° (b) 20° (c) 320° (d) 140°
  38. 38.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 110° (b) 150° (c) 70° (d) 100°
  39. 39.Two angles of a triangle are 35° and 95°. What is the exterior angle at the third corner? (a) 130° (b) 85° (c) 50° (d) 145°
  40. 40.Two angles of a triangle are 40° and 60°. What is the third angle? (a) 80° (b) 120° (c) 100° (d) 140°

Answer key

  1. 130°
  2. 30°
  3. 75°
  4. 125°
  5. 120°
  6. 60°
  7. 100°
  8. 85°
  9. 140°
  10. 115°
  11. 125°
  12. 95°
  13. 75°
  14. 90°
  15. 40°
  16. 85°
  17. 10°
  18. 135°
  19. 55°
  20. 130°
  21. 50°
  22. 50°
  23. 65°
  24. 60°
  25. 60°
  26. 80°
  27. 100°
  28. 25°
  29. 115°
  30. 60°
  31. 140°
  32. 150°
  33. 110°
  34. 20°
  35. 10°
  36. 125°
  37. 160°
  38. 70°
  39. 130°
  40. 80°

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