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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 256 · 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. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 260° (b) 80° (c) 130° (d) 50°
  2. 2.Two angles of a triangle are 45° and 55°. What is the third angle? (a) 100° (b) 80° (c) 125° (d) 135°
  3. 3.Two angles of a triangle are 35° and 90°. What is the third angle? (a) 125° (b) 90° (c) 145° (d) 55°
  4. 4.Two angles of a triangle are 30° and 110°. What is the exterior angle at the third corner? (a) 70° (b) 150° (c) 140° (d) 40°
  5. 5.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 60° (b) 140° (c) 100° (d) 120°
  6. 6.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 60° (b) 145° (c) 155° (d) 120°
  7. 7.Two angles of a triangle are 40° and 75°. What is the exterior angle at the third corner? (a) 140° (b) 115° (c) 65° (d) 105°
  8. 8.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 285° (b) 105° (c) 75° (d) 15°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 40° (b) 160° (c) 20° (d) 21°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 26° (b) 25° (c) 155° (d) 50°
  11. 11.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 100° (b) 150° (c) 130° (d) 80°
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 59° (b) 120° (c) 60° (d) 61°
  13. 13.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 140° (b) 100° (c) 60° (d) 120°
  14. 14.Two angles of a triangle are 40° and 45°. What is the third angle? (a) 135° (b) 140° (c) 85° (d) 95°
  15. 15.Two angles of a triangle are 60° and 55°. What is the exterior angle at the third corner? (a) 120° (b) 65° (c) 125° (d) 115°
  16. 16.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 30° (b) 110° (c) 100° (d) 150°
  17. 17.Two angles of a triangle are 50° and 50°. What is the third angle? (a) 100° (b) 130° (c) 260° (d) 80°
  18. 18.Two angles of a triangle are 70° and 90°. What is the third angle? (a) 110° (b) 90° (c) 160° (d) 20°
  19. 19.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 135° (b) 120° (c) 105° (d) 75°
  20. 20.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 25° (c) 65° (d) 155°
  21. 21.Two angles of a triangle are 30° and 120°. What is the exterior angle at the third corner? (a) 150° (b) 210° (c) 30° (d) 60°
  22. 22.Two angles of a triangle are 30° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 255° (c) 150° (d) 75°
  23. 23.Two angles of a triangle are 75° and 60°. What is the third angle? (a) 45° (b) 105° (c) 120° (d) 135°
  24. 24.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 45° (c) 135° (d) 90°
  25. 25.Two angles of a triangle are 35° and 25°. What is the third angle? (a) 155° (b) 120° (c) 145° (d) 60°
  26. 26.Two angles of a triangle are 60° and 85°. What is the third angle? (a) 95° (b) 120° (c) 35° (d) 145°
  27. 27.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 35° (b) 90° (c) 145° (d) 125°
  28. 28.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 80° (c) 40° (d) 50°
  29. 29.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 25° (b) 130° (c) 50° (d) 35°
  30. 30.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 300° (b) 60° (c) 30° (d) 120°
  31. 31.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 340° (b) 20° (c) 160° (d) 70°
  32. 32.Two angles of a triangle are 75° and 45°. What is the exterior angle at the third corner? (a) 60° (b) 105° (c) 135° (d) 120°
  33. 33.Two angles of a triangle are 25° and 20°. What is the third angle? (a) 135° (b) 45° (c) 155° (d) 160°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 85° (b) 190° (c) 10° (d) 95°
  35. 35.Two angles of a triangle are 55° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 125° (c) 90° (d) 270°
  36. 36.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 46° (c) 90° (d) 45°
  37. 37.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 105° (b) 255° (c) 76° (d) 75°
  38. 38.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°
  39. 39.Two angles of a triangle are 30° and 80°. What is the third angle? (a) 150° (b) 110° (c) 70° (d) 100°
  40. 40.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 40° (c) 50° (d) 65°

Answer key

  1. 130°
  2. 80°
  3. 55°
  4. 140°
  5. 120°
  6. 120°
  7. 115°
  8. 105°
  9. 20°
  10. 25°
  11. 100°
  12. 60°
  13. 60°
  14. 95°
  15. 115°
  16. 150°
  17. 80°
  18. 20°
  19. 75°
  20. 130°
  21. 150°
  22. 105°
  23. 45°
  24. 90°
  25. 120°
  26. 35°
  27. 145°
  28. 40°
  29. 25°
  30. 120°
  31. 160°
  32. 120°
  33. 135°
  34. 95°
  35. 90°
  36. 45°
  37. 75°
  38. 45°
  39. 70°
  40. 65°

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