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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 557 · 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 75° and 30°. What is the third angle? (a) 150° (b) 75° (c) 105° (d) 255°
  2. 2.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 150° (b) 30° (c) 60° (d) 330°
  3. 3.Two angles of a triangle are 60° and 70°. What is the exterior angle at the third corner? (a) 130° (b) 50° (c) 110° (d) 120°
  4. 4.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 30° (c) 105° (d) 75°
  5. 5.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 120° (c) 110° (d) 60°
  6. 6.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 130° (b) 230° (c) 51° (d) 50°
  7. 7.Two angles of a triangle are 75° and 60°. What is the third angle? (a) 135° (b) 45° (c) 105° (d) 120°
  8. 8.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 50° (b) 120° (c) 110° (d) 130°
  9. 9.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 145° (b) 115° (c) 100° (d) 35°
  10. 10.Two angles of a triangle are 70° and 75°. What is the third angle? (a) 35° (b) 105° (c) 110° (d) 145°
  11. 11.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 50° (c) 25° (d) 130°
  12. 12.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 205° (b) 26° (c) 25° (d) 155°
  13. 13.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 10° (c) 85° (d) 95°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 75° (b) 105° (c) 210° (d) 30°
  15. 15.Two angles of a triangle are 20° and 90°. What is the third angle? (a) 90° (b) 160° (c) 70° (d) 110°
  16. 16.Two angles of a triangle are 20° and 20°. What is the third angle? (a) 160° (b) 140° (c) 320° (d) 40°
  17. 17.Two angles of a triangle are 70° and 25°. What is the third angle? (a) 110° (b) 85° (c) 95° (d) 155°
  18. 18.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 135° (b) 110° (c) 115° (d) 70°
  19. 19.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 120° (b) 140° (c) 60° (d) 100°
  20. 20.Two angles of a triangle are 20° and 140°. What is the third angle? (a) 200° (b) 20° (c) 40° (d) 160°
  21. 21.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 40° (c) 140° (d) 20°
  22. 22.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 70° (c) 110° (d) 105°
  23. 23.Two angles of a triangle are 50° and 45°. What is the third angle? (a) 85° (b) 135° (c) 130° (d) 95°
  24. 24.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 25° (c) 65° (d) 115°
  25. 25.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 81° (b) 80° (c) 100° (d) 260°
  26. 26.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 165° (b) 110° (c) 15° (d) 85°
  27. 27.Two angles of a triangle are 25° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 155° (c) 60° (d) 120°
  28. 28.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 66° (b) 65° (c) 245° (d) 115°
  29. 29.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 80° (c) 50° (d) 10°
  30. 30.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 50° (c) 100° (d) 80°
  31. 31.Two angles of a triangle are 55° and 95°. What is the third angle? (a) 150° (b) 30° (c) 125° (d) 85°
  32. 32.Two angles of a triangle are 55° and 25°. What is the exterior angle at the third corner? (a) 80° (b) 125° (c) 155° (d) 100°
  33. 33.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 100° (b) 105° (c) 155° (d) 80°
  34. 34.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 280° (b) 10° (c) 80° (d) 100°
  35. 35.Two angles of a triangle are 30° and 85°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 95° (d) 150°
  36. 36.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 140° (c) 70° (d) 50°
  37. 37.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 120° (b) 300° (c) 30° (d) 60°
  38. 38.Two angles of a triangle are 60° and 65°. What is the third angle? (a) 115° (b) 120° (c) 55° (d) 125°
  39. 39.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 265° (c) 95° (d) 85°
  40. 40.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 75° (b) 100° (c) 105° (d) 155°

Answer key

  1. 75°
  2. 150°
  3. 130°
  4. 30°
  5. 120°
  6. 50°
  7. 45°
  8. 130°
  9. 35°
  10. 35°
  11. 25°
  12. 25°
  13. 10°
  14. 105°
  15. 70°
  16. 140°
  17. 85°
  18. 70°
  19. 60°
  20. 20°
  21. 20°
  22. 110°
  23. 85°
  24. 50°
  25. 80°
  26. 15°
  27. 120°
  28. 65°
  29. 50°
  30. 40°
  31. 30°
  32. 80°
  33. 80°
  34. 100°
  35. 115°
  36. 70°
  37. 120°
  38. 55°
  39. 85°
  40. 75°

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