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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 171 · 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 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) 41° (d) 40°
  2. 2.Two angles of a triangle are 25° and 100°. What is the third angle? (a) 155° (b) 125° (c) 80° (d) 55°
  3. 3.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 120° (b) 61° (c) 240° (d) 60°
  4. 4.Two angles of a triangle are 30° and 60°. What is the third angle? (a) 120° (b) 270° (c) 90° (d) 150°
  5. 5.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 60° (c) 120° (d) 110°
  6. 6.Two angles of a triangle are 60° and 75°. What is the third angle? (a) 45° (b) 135° (c) 105° (d) 120°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 150° (c) 15° (d) 25°
  8. 8.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 255° (b) 105° (c) 75° (d) 150°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 145° (b) 35° (c) 36° (d) 70°
  10. 10.Two angles of a triangle are 65° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 105° (c) 115° (d) 75°
  11. 11.Two angles of a triangle are 75° and 45°. What is the exterior angle at the third corner? (a) 105° (b) 60° (c) 120° (d) 135°
  12. 12.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 140° (b) 110° (c) 70° (d) 250°
  13. 13.Two angles of a triangle are 25° and 115°. What is the exterior angle at the third corner? (a) 140° (b) 40° (c) 155° (d) 65°
  14. 14.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 40° (b) 140° (c) 50° (d) 320°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 71° (b) 140° (c) 110° (d) 70°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 60° (c) 120° (d) 30°
  17. 17.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 145° (c) 120° (d) 60°
  18. 18.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 155° (b) 205° (c) 26° (d) 25°
  19. 19.Two angles of a triangle are 40° and 105°. What is the exterior angle at the third corner? (a) 145° (b) 75° (c) 140° (d) 35°
  20. 20.Two angles of a triangle are 30° and 20°. What is the third angle? (a) 160° (b) 150° (c) 130° (d) 50°
  21. 21.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 150° (b) 105° (c) 210° (d) 30°
  22. 22.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 105° (b) 145° (c) 75° (d) 110°
  23. 23.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 35° (c) 130° (d) 25°
  24. 24.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 125° (b) 55° (c) 235° (d) 56°
  25. 25.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 25° (c) 65° (d) 50°
  26. 26.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 130° (b) 25° (c) 155° (d) 310°
  27. 27.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 70° (b) 35° (c) 215° (d) 145°
  28. 28.Two angles of a triangle are 45° and 60°. What is the third angle? (a) 120° (b) 135° (c) 105° (d) 75°
  29. 29.Two angles of a triangle are 20° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 40° (c) 320° (d) 140°
  30. 30.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 115° (b) 35° (c) 145° (d) 100°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 130° (c) 40° (d) 50°
  32. 32.Two angles of a triangle are 70° and 70°. What is the exterior angle at the third corner? (a) 40° (b) 220° (c) 140° (d) 110°
  33. 33.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 75° (c) 150° (d) 30°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 45° (b) 90° (c) 135° (d) 270°
  35. 35.Two angles of a triangle are 50° and 55°. What is the third angle? (a) 105° (b) 130° (c) 125° (d) 75°
  36. 36.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 75° (c) 15° (d) 30°
  37. 37.Two angles of a triangle are 45° and 25°. What is the third angle? (a) 70° (b) 155° (c) 135° (d) 110°
  38. 38.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 95° (c) 10° (d) 5°
  39. 39.Two angles of a triangle are 70° and 45°. What is the exterior angle at the third corner? (a) 115° (b) 110° (c) 135° (d) 65°
  40. 40.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 70° (b) 290° (c) 145° (d) 110°

Answer key

  1. 40°
  2. 55°
  3. 60°
  4. 90°
  5. 120°
  6. 45°
  7. 15°
  8. 105°
  9. 35°
  10. 105°
  11. 120°
  12. 70°
  13. 140°
  14. 140°
  15. 70°
  16. 60°
  17. 60°
  18. 25°
  19. 145°
  20. 130°
  21. 30°
  22. 75°
  23. 25°
  24. 55°
  25. 50°
  26. 155°
  27. 35°
  28. 75°
  29. 40°
  30. 145°
  31. 65°
  32. 140°
  33. 75°
  34. 135°
  35. 75°
  36. 30°
  37. 110°
  38. 10°
  39. 115°
  40. 70°

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