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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 102 · 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 45° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 95° (c) 135° (d) 85°
  2. 2.Two angles of a triangle are 60° and 75°. What is the third angle? (a) 120° (b) 105° (c) 45° (d) 135°
  3. 3.Two angles of a triangle are 30° and 135°. What is the third angle? (a) 165° (b) 15° (c) 150° (d) 45°
  4. 4.Two angles of a triangle are 50° and 45°. What is the third angle? (a) 95° (b) 130° (c) 135° (d) 85°
  5. 5.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 61° (c) 30° (d) 60°
  6. 6.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 35° (c) 145° (d) 55°
  7. 7.Two angles of a triangle are 35° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 110° (c) 145° (d) 70°
  8. 8.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 16° (b) 15° (c) 165° (d) 195°
  9. 9.Two angles of a triangle are 55° and 30°. What is the third angle? (a) 85° (b) 125° (c) 95° (d) 150°
  10. 10.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 115° (b) 65° (c) 145° (d) 100°
  11. 11.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) 85° (c) 86° (d) 95°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 15° (c) 25° (d) 30°
  13. 13.Two angles of a triangle are 50° and 95°. What is the exterior angle at the third corner? (a) 35° (b) 130° (c) 145° (d) 85°
  14. 14.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 110° (b) 105° (c) 70° (d) 145°
  15. 15.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 120° (c) 125° (d) 55°
  16. 16.Two angles of a triangle are 65° and 105°. What is the third angle? (a) 10° (b) 75° (c) 170° (d) 115°
  17. 17.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 60° (b) 150° (c) 330° (d) 30°
  18. 18.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 260° (b) 81° (c) 100° (d) 80°
  19. 19.Two angles of a triangle are 60° and 20°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 120° (d) 160°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 280° (c) 100° (d) 140°
  21. 21.Two angles of a triangle are 45° and 75°. What is the third angle? (a) 60° (b) 105° (c) 120° (d) 135°
  22. 22.Two angles of a triangle are 35° and 80°. What is the third angle? (a) 65° (b) 100° (c) 145° (d) 115°
  23. 23.Two angles of a triangle are 60° and 110°. What is the third angle? (a) 70° (b) 170° (c) 120° (d) 10°
  24. 24.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 60° (c) 145° (d) 120°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 60° (c) 75° (d) 30°
  26. 26.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 35° (c) 70° (d) 55°
  27. 27.Two angles of a triangle are 45° and 60°. What is the third angle? (a) 105° (b) 120° (c) 135° (d) 75°
  28. 28.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 10° (b) 280° (c) 80° (d) 100°
  29. 29.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 45° (c) 35° (d) 110°
  30. 30.Two angles of a triangle are 30° and 55°. What is the exterior angle at the third corner? (a) 150° (b) 125° (c) 85° (d) 95°
  31. 31.Two angles of a triangle are 55° and 105°. What is the third angle? (a) 75° (b) 160° (c) 125° (d) 20°
  32. 32.Two angles of a triangle are 75° and 30°. What is the third angle? (a) 75° (b) 150° (c) 255° (d) 105°
  33. 33.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 11° (c) 160° (d) 10°
  34. 34.Two angles of a triangle are 45° and 70°. What is the third angle? (a) 65° (b) 135° (c) 115° (d) 110°
  35. 35.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 105° (b) 120° (c) 75° (d) 135°
  36. 36.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 40° (c) 100° (d) 80°
  37. 37.Two angles of a triangle are 55° and 60°. What is the exterior angle at the third corner? (a) 115° (b) 125° (c) 120° (d) 65°
  38. 38.Two angles of a triangle are 30° and 65°. What is the third angle? (a) 115° (b) 95° (c) 85° (d) 150°
  39. 39.Two angles of a triangle are 20° and 90°. What is the third angle? (a) 90° (b) 110° (c) 160° (d) 70°
  40. 40.Two angles of a triangle are 70° and 45°. What is the exterior angle at the third corner? (a) 110° (b) 115° (c) 65° (d) 135°

Answer key

  1. 85°
  2. 45°
  3. 15°
  4. 85°
  5. 60°
  6. 110°
  7. 110°
  8. 15°
  9. 95°
  10. 65°
  11. 85°
  12. 15°
  13. 145°
  14. 70°
  15. 125°
  16. 10°
  17. 150°
  18. 80°
  19. 80°
  20. 140°
  21. 60°
  22. 65°
  23. 10°
  24. 60°
  25. 75°
  26. 70°
  27. 75°
  28. 100°
  29. 35°
  30. 85°
  31. 20°
  32. 75°
  33. 10°
  34. 65°
  35. 75°
  36. 40°
  37. 115°
  38. 85°
  39. 70°
  40. 115°

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