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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 136 · 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 20°. What is each of the other two angles? (a) 160° (b) 80° (c) 70° (d) 20°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 30° (c) 120° (d) 60°
  3. 3.Two angles of a triangle are 45° and 85°. What is the exterior angle at the third corner? (a) 50° (b) 135° (c) 130° (d) 95°
  4. 4.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 115° (b) 150° (c) 30° (d) 95°
  5. 5.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 120° (b) 95° (c) 35° (d) 145°
  6. 6.Two angles of a triangle are 25° and 45°. What is the exterior angle at the third corner? (a) 110° (b) 135° (c) 155° (d) 70°
  7. 7.Two angles of a triangle are 55° and 95°. What is the third angle? (a) 30° (b) 85° (c) 150° (d) 125°
  8. 8.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 170° (b) 85° (c) 10° (d) 105°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 41° (b) 40° (c) 80° (d) 140°
  10. 10.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 80° (b) 150° (c) 110° (d) 100°
  11. 11.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 115° (b) 125° (c) 60° (d) 120°
  12. 12.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 20° (c) 100° (d) 10°
  13. 13.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 100° (c) 75° (d) 155°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 20° (c) 40° (d) 30°
  15. 15.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 150° (c) 135° (d) 30°
  16. 16.Two angles of a triangle are 25° and 90°. What is the exterior angle at the third corner? (a) 65° (b) 90° (c) 115° (d) 155°
  17. 17.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 85° (b) 95° (c) 275° (d) 5°
  18. 18.Two angles of a triangle are 20° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 45° (c) 135° (d) 160°
  19. 19.Two angles of a triangle are 60° and 55°. What is the third angle? (a) 115° (b) 65° (c) 125° (d) 120°
  20. 20.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 110° (d) 150°
  21. 21.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 35° (c) 55° (d) 110°
  22. 22.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 270° (b) 125° (c) 90° (d) 145°
  23. 23.Two angles of a triangle are 50° and 110°. What is the third angle? (a) 70° (b) 130° (c) 160° (d) 20°
  24. 24.Two angles of a triangle are 75° and 80°. What is the third angle? (a) 105° (b) 100° (c) 155° (d) 25°
  25. 25.Two angles of a triangle are 60° and 65°. What is the third angle? (a) 115° (b) 55° (c) 125° (d) 120°
  26. 26.Two angles of a triangle are 65° and 25°. What is the third angle? (a) 155° (b) 115° (c) 90° (d) 270°
  27. 27.Two angles of a triangle are 35° and 85°. What is the exterior angle at the third corner? (a) 60° (b) 95° (c) 120° (d) 145°
  28. 28.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 86° (c) 85° (d) 95°
  29. 29.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 105° (b) 125° (c) 160° (d) 75°
  30. 30.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°
  31. 31.Two angles of a triangle are 20° and 40°. What is the third angle? (a) 60° (b) 160° (c) 120° (d) 140°
  32. 32.Two angles of a triangle are 45° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 135° (c) 80° (d) 100°
  33. 33.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 55° (b) 130° (c) 125° (d) 105°
  34. 34.Two angles of a triangle are 55° and 105°. What is the third angle? (a) 20° (b) 125° (c) 75° (d) 160°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 130° (b) 50° (c) 100° (d) 51°
  36. 36.Two angles of a triangle are 55° and 80°. What is the exterior angle at the third corner? (a) 45° (b) 100° (c) 135° (d) 125°
  37. 37.Two angles of a triangle are 45° and 50°. What is the exterior angle at the third corner? (a) 85° (b) 135° (c) 130° (d) 95°
  38. 38.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 125° (b) 110° (c) 55° (d) 235°
  39. 39.Two angles of a triangle are 55° and 25°. What is the third angle? (a) 125° (b) 155° (c) 100° (d) 80°
  40. 40.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 155° (b) 105° (c) 100° (d) 75°

Answer key

  1. 80°
  2. 30°
  3. 130°
  4. 150°
  5. 145°
  6. 70°
  7. 30°
  8. 10°
  9. 40°
  10. 80°
  11. 60°
  12. 20°
  13. 105°
  14. 20°
  15. 150°
  16. 115°
  17. 95°
  18. 45°
  19. 65°
  20. 100°
  21. 110°
  22. 90°
  23. 20°
  24. 25°
  25. 55°
  26. 90°
  27. 120°
  28. 85°
  29. 75°
  30. 150°
  31. 120°
  32. 80°
  33. 125°
  34. 20°
  35. 50°
  36. 135°
  37. 95°
  38. 55°
  39. 100°
  40. 75°

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