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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 115 · 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 angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 50° (c) 80° (d) 40°
  2. 2.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 250° (b) 125° (c) 70° (d) 55°
  3. 3.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 30° (c) 150° (d) 100°
  4. 4.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 60° (b) 140° (c) 100° (d) 120°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 60° (b) 120° (c) 30° (d) 70°
  6. 6.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 5° (c) 10° (d) 85°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 70° (b) 110° (c) 220° (d) 40°
  8. 8.Two angles of a triangle are 25° and 125°. What is the third angle? (a) 30° (b) 155° (c) 150° (d) 55°
  9. 9.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 120° (c) 60° (d) 61°
  10. 10.Two angles of a triangle are 65° and 55°. What is the exterior angle at the third corner? (a) 115° (b) 60° (c) 120° (d) 125°
  11. 11.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 100° (c) 40° (d) 140°
  12. 12.Two angles of a triangle are 25° and 45°. What is the third angle? (a) 110° (b) 135° (c) 155° (d) 70°
  13. 13.Two angles of a triangle are 25° and 30°. What is the third angle? (a) 125° (b) 55° (c) 150° (d) 155°
  14. 14.Two angles of a triangle are 25° and 25°. What is the third angle? (a) 310° (b) 50° (c) 155° (d) 130°
  15. 15.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 40° (b) 15° (c) 165° (d) 155°
  16. 16.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 80° (c) 20° (d) 10°
  17. 17.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 66° (b) 115° (c) 245° (d) 65°
  18. 18.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 75° (c) 30° (d) 105°
  19. 19.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 40° (c) 130° (d) 80°
  20. 20.Two angles of a triangle are 55° and 25°. What is the third angle? (a) 125° (b) 100° (c) 80° (d) 155°
  21. 21.Two angles of a triangle are 25° and 80°. What is the third angle? (a) 155° (b) 100° (c) 75° (d) 105°
  22. 22.Two angles of a triangle are 70° and 75°. What is the third angle? (a) 110° (b) 35° (c) 145° (d) 105°
  23. 23.Two angles of a triangle are 40° and 90°. What is the third angle? (a) 130° (b) 140° (c) 50° (d) 90°
  24. 24.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 100° (b) 80° (c) 155° (d) 105°
  25. 25.Two angles of a triangle are 60° and 20°. What is the third angle? (a) 80° (b) 160° (c) 120° (d) 100°
  26. 26.Two angles of a triangle are 55° and 90°. What is the third angle? (a) 125° (b) 35° (c) 90° (d) 145°
  27. 27.Two angles of a triangle are 25° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 155° (c) 105° (d) 75°
  28. 28.Two angles of a triangle are 80° and 65°. What is the third angle? (a) 115° (b) 100° (c) 145° (d) 35°
  29. 29.Two angles of a triangle are 70° and 20°. What is the third angle? (a) 160° (b) 110° (c) 90° (d) 270°
  30. 30.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 160° (c) 80° (d) 70°
  31. 31.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 70° (b) 55° (c) 125° (d) 35°
  32. 32.Two angles of a triangle are 60° and 55°. What is the exterior angle at the third corner? (a) 65° (b) 125° (c) 120° (d) 115°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 150° (b) 76° (c) 105° (d) 75°
  34. 34.Two angles of a triangle are 25° and 45°. What is the exterior angle at the third corner? (a) 110° (b) 155° (c) 135° (d) 70°
  35. 35.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 15° (b) 105° (c) 285° (d) 75°
  36. 36.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 150° (c) 30° (d) 60°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 130° (b) 310° (c) 25° (d) 155°
  38. 38.Two angles of a triangle are 40° and 85°. What is the third angle? (a) 140° (b) 125° (c) 95° (d) 55°
  39. 39.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 135° (b) 100° (c) 45° (d) 125°
  40. 40.Two angles of a triangle are 45° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 135° (c) 50° (d) 130°

Answer key

  1. 40°
  2. 125°
  3. 150°
  4. 120°
  5. 60°
  6. 10°
  7. 110°
  8. 30°
  9. 60°
  10. 120°
  11. 100°
  12. 110°
  13. 125°
  14. 130°
  15. 15°
  16. 20°
  17. 65°
  18. 30°
  19. 80°
  20. 100°
  21. 75°
  22. 35°
  23. 50°
  24. 80°
  25. 100°
  26. 35°
  27. 105°
  28. 35°
  29. 90°
  30. 80°
  31. 70°
  32. 115°
  33. 75°
  34. 70°
  35. 105°
  36. 120°
  37. 155°
  38. 55°
  39. 45°
  40. 130°

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