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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 96 · 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 35° and 125°. What is the third angle? (a) 145° (b) 160° (c) 20° (d) 55°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 50° (c) 10° (d) 100°
  3. 3.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 110° (b) 160° (c) 130° (d) 70°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 66° (b) 130° (c) 65° (d) 115°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 55° (c) 46° (d) 90°
  6. 6.Two angles of a triangle are 60° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 120° (c) 270° (d) 90°
  7. 7.Two angles of a triangle are 70° and 60°. What is the third angle? (a) 120° (b) 110° (c) 130° (d) 50°
  8. 8.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 45° (c) 155° (d) 135°
  9. 9.Two angles of a triangle are 75° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 105° (c) 65° (d) 115°
  10. 10.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 25° (c) 130° (d) 65°
  11. 11.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 100° (b) 60° (c) 140° (d) 120°
  12. 12.Two angles of a triangle are 60° and 20°. What is the third angle? (a) 100° (b) 160° (c) 120° (d) 80°
  13. 13.Two angles of a triangle are 65° and 60°. What is the exterior angle at the third corner? (a) 115° (b) 120° (c) 55° (d) 125°
  14. 14.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 30° (c) 75° (d) 105°
  15. 15.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 130° (b) 310° (c) 40° (d) 50°
  16. 16.Two angles of a triangle are 40° and 75°. What is the exterior angle at the third corner? (a) 140° (b) 115° (c) 105° (d) 65°
  17. 17.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 60° (b) 110° (c) 120° (d) 130°
  18. 18.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 40° (c) 130° (d) 80°
  19. 19.Two angles of a triangle are 75° and 45°. What is the third angle? (a) 60° (b) 105° (c) 135° (d) 120°
  20. 20.Two angles of a triangle are 50° and 65°. What is the exterior angle at the third corner? (a) 65° (b) 245° (c) 130° (d) 115°
  21. 21.Two angles of a triangle are 75° and 80°. What is the third angle? (a) 105° (b) 100° (c) 25° (d) 155°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 160° (b) 100° (c) 81° (d) 80°
  23. 23.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 71° (b) 250° (c) 110° (d) 70°
  24. 24.Two angles of a triangle are 30° and 45°. What is the third angle? (a) 75° (b) 150° (c) 105° (d) 135°
  25. 25.Two angles of a triangle are 65° and 45°. What is the exterior angle at the third corner? (a) 110° (b) 115° (c) 135° (d) 70°
  26. 26.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 85° (c) 10° (d) 5°
  27. 27.Two angles of a triangle are 65° and 105°. What is the third angle? (a) 115° (b) 170° (c) 75° (d) 10°
  28. 28.Two angles of a triangle are 20° and 115°. What is the third angle? (a) 45° (b) 65° (c) 160° (d) 135°
  29. 29.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 20° (b) 140° (c) 40° (d) 30°
  30. 30.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 20° (c) 55° (d) 70°
  31. 31.Two angles of a triangle are 55° and 110°. What is the third angle? (a) 165° (b) 125° (c) 70° (d) 15°
  32. 32.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 140° (c) 100° (d) 40°
  33. 33.Two angles of a triangle are 40° and 125°. What is the third angle? (a) 55° (b) 15° (c) 165° (d) 140°
  34. 34.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) 150° (d) 60°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 70° (c) 160° (d) 80°
  36. 36.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 60° (c) 30° (d) 120°
  37. 37.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 230° (b) 130° (c) 115° (d) 50°
  38. 38.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 60° (b) 30° (c) 120° (d) 300°
  39. 39.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 150° (b) 105° (c) 30° (d) 210°
  40. 40.Two angles of a triangle are 40° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 80° (c) 280° (d) 100°

Answer key

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

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