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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 413 · 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 straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 115° (b) 245° (c) 66° (d) 65°
  2. 2.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 170° (b) 10° (c) 105° (d) 85°
  3. 3.Two angles of a triangle are 80° and 55°. What is the third angle? (a) 45° (b) 100° (c) 125° (d) 135°
  4. 4.Two angles of a triangle are 20° and 40°. What is the third angle? (a) 160° (b) 60° (c) 140° (d) 120°
  5. 5.Two angles of a triangle are 20° and 105°. What is the third angle? (a) 160° (b) 75° (c) 55° (d) 125°
  6. 6.Two angles of a triangle are 60° and 50°. What is the exterior angle at the third corner? (a) 120° (b) 130° (c) 110° (d) 70°
  7. 7.Two angles of a triangle are 75° and 80°. What is the third angle? (a) 25° (b) 105° (c) 100° (d) 155°
  8. 8.Two angles of a triangle are 50° and 45°. What is the third angle? (a) 135° (b) 130° (c) 85° (d) 95°
  9. 9.Two angles of a triangle are 25° and 120°. What is the third angle? (a) 60° (b) 145° (c) 155° (d) 35°
  10. 10.Two angles of a triangle are 50° and 110°. What is the third angle? (a) 20° (b) 70° (c) 130° (d) 160°
  11. 11.Two angles of a triangle are 60° and 105°. What is the third angle? (a) 75° (b) 120° (c) 165° (d) 15°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 120° (c) 30° (d) 60°
  13. 13.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°
  14. 14.Two angles of a triangle are 55° and 20°. What is the third angle? (a) 75° (b) 105° (c) 160° (d) 125°
  15. 15.Two angles of a triangle are 45° and 100°. What is the exterior angle at the third corner? (a) 35° (b) 80° (c) 145° (d) 135°
  16. 16.Two angles of a triangle are 55° and 25°. What is the third angle? (a) 80° (b) 125° (c) 100° (d) 155°
  17. 17.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 80° (c) 50° (d) 40°
  18. 18.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 115° (b) 65° (c) 105° (d) 140°
  19. 19.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) 75° (d) 285°
  20. 20.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 120° (b) 60° (c) 30° (d) 40°
  21. 21.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 155° (b) 80° (c) 100° (d) 105°
  22. 22.Two angles of a triangle are 20° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 160° (c) 60° (d) 120°
  23. 23.Two angles of a triangle are 25° and 50°. What is the third angle? (a) 130° (b) 75° (c) 155° (d) 105°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 51° (b) 130° (c) 50° (d) 100°
  25. 25.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 305° (b) 125° (c) 55° (d) 35°
  26. 26.Two angles of a triangle are 65° and 45°. What is the exterior angle at the third corner? (a) 115° (b) 135° (c) 110° (d) 70°
  27. 27.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) 300° (c) 30° (d) 120°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 65° (b) 66° (c) 130° (d) 115°
  29. 29.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 155° (c) 130° (d) 65°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 30° (b) 16° (c) 165° (d) 15°
  31. 31.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 10° (c) 5° (d) 85°
  32. 32.Two angles of a triangle are 45° and 95°. What is the exterior angle at the third corner? (a) 140° (b) 40° (c) 135° (d) 85°
  33. 33.Two angles of a triangle are 45° and 105°. What is the third angle? (a) 135° (b) 30° (c) 75° (d) 150°
  34. 34.Two angles of a triangle are 80° and 50°. What is the exterior angle at the third corner? (a) 100° (b) 130° (c) 230° (d) 50°
  35. 35.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 125° (b) 115° (c) 120° (d) 60°
  36. 36.Two angles of a triangle are 45° and 30°. What is the third angle? (a) 150° (b) 135° (c) 75° (d) 105°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 10° (b) 160° (c) 11° (d) 20°
  38. 38.Two angles of a triangle are 65° and 50°. What is the third angle? (a) 130° (b) 115° (c) 65° (d) 245°
  39. 39.Two angles of a triangle are 35° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 70° (c) 110° (d) 145°
  40. 40.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 105° (b) 145° (c) 140° (d) 75°

Answer key

  1. 65°
  2. 10°
  3. 45°
  4. 120°
  5. 55°
  6. 110°
  7. 25°
  8. 85°
  9. 35°
  10. 20°
  11. 15°
  12. 60°
  13. 125°
  14. 105°
  15. 145°
  16. 100°
  17. 80°
  18. 65°
  19. 105°
  20. 30°
  21. 80°
  22. 120°
  23. 105°
  24. 50°
  25. 125°
  26. 110°
  27. 120°
  28. 65°
  29. 130°
  30. 15°
  31. 10°
  32. 140°
  33. 30°
  34. 130°
  35. 60°
  36. 105°
  37. 10°
  38. 65°
  39. 110°
  40. 75°

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