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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 93 · 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 60° and 40°. What is the exterior angle at the third corner? (a) 120° (b) 80° (c) 140° (d) 100°
  2. 2.Two angles of a triangle are 65° and 105°. What is the third angle? (a) 170° (b) 115° (c) 10° (d) 75°
  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) 240° (b) 61° (c) 60° (d) 120°
  4. 4.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 35° (c) 110° (d) 45°
  5. 5.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 30° (c) 60° (d) 61°
  6. 6.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 135° (c) 91° (d) 45°
  7. 7.Two angles of a triangle are 45° and 80°. What is the exterior angle at the third corner? (a) 135° (b) 55° (c) 100° (d) 125°
  8. 8.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 100° (c) 10° (d) 50°
  9. 9.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 65° (b) 245° (c) 115° (d) 66°
  10. 10.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 125° (b) 130° (c) 55° (d) 105°
  11. 11.Two angles of a triangle are 55° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 125° (c) 85° (d) 95°
  12. 12.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 155° (b) 95° (c) 85° (d) 120°
  13. 13.Two angles of a triangle are 25° and 95°. What is the third angle? (a) 85° (b) 155° (c) 60° (d) 120°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 110° (b) 56° (c) 55° (d) 125°
  15. 15.Two angles of a triangle are 60° and 90°. What is the third angle? (a) 90° (b) 150° (c) 30° (d) 120°
  16. 16.Two angles of a triangle are 45° and 25°. What is the exterior angle at the third corner? (a) 135° (b) 70° (c) 110° (d) 155°
  17. 17.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 90° (b) 270° (c) 140° (d) 130°
  18. 18.Two angles of a triangle are 55° and 75°. What is the exterior angle at the third corner? (a) 125° (b) 50° (c) 130° (d) 105°
  19. 19.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 75° (b) 145° (c) 140° (d) 105°
  20. 20.Two angles of a triangle are 45° and 40°. What is the exterior angle at the third corner? (a) 95° (b) 140° (c) 85° (d) 135°
  21. 21.Two angles of a triangle are 65° and 30°. What is the exterior angle at the third corner? (a) 85° (b) 150° (c) 115° (d) 95°
  22. 22.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 30° (b) 150° (c) 330° (d) 60°
  23. 23.Two angles of a triangle are 35° and 115°. What is the third angle? (a) 65° (b) 30° (c) 145° (d) 150°
  24. 24.Two angles of a triangle are 75° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 105° (c) 120° (d) 60°
  25. 25.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 76° (b) 105° (c) 75° (d) 150°
  26. 26.Two angles of a triangle are 60° and 45°. What is the exterior angle at the third corner? (a) 105° (b) 135° (c) 75° (d) 120°
  27. 27.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 65° (c) 145° (d) 150°
  28. 28.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 90° (c) 46° (d) 55°
  29. 29.Two angles of a triangle are 25° and 115°. What is the third angle? (a) 40° (b) 155° (c) 65° (d) 140°
  30. 30.Two angles of a triangle are 75° and 60°. What is the third angle? (a) 45° (b) 135° (c) 120° (d) 105°
  31. 31.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 130° (c) 80° (d) 40°
  32. 32.Two angles of a triangle are 65° and 85°. What is the third angle? (a) 115° (b) 150° (c) 30° (d) 95°
  33. 33.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 35° (c) 110° (d) 145°
  34. 34.Two angles of a triangle are 60° and 105°. What is the third angle? (a) 15° (b) 120° (c) 75° (d) 165°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 80° (c) 130° (d) 260°
  36. 36.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 140° (c) 20° (d) 40°
  37. 37.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 5° (c) 95° (d) 10°
  38. 38.Two angles of a triangle are 50° and 115°. What is the third angle? (a) 165° (b) 15° (c) 65° (d) 130°
  39. 39.Two angles of a triangle are 65° and 40°. What is the third angle? (a) 115° (b) 140° (c) 105° (d) 75°
  40. 40.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 140° (c) 95° (d) 85°

Answer key

  1. 100°
  2. 10°
  3. 60°
  4. 35°
  5. 60°
  6. 90°
  7. 125°
  8. 50°
  9. 65°
  10. 55°
  11. 95°
  12. 95°
  13. 60°
  14. 55°
  15. 30°
  16. 70°
  17. 90°
  18. 130°
  19. 75°
  20. 85°
  21. 95°
  22. 150°
  23. 30°
  24. 120°
  25. 75°
  26. 105°
  27. 65°
  28. 45°
  29. 40°
  30. 45°
  31. 80°
  32. 30°
  33. 110°
  34. 15°
  35. 130°
  36. 20°
  37. 10°
  38. 15°
  39. 75°
  40. 85°

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