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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 199 · 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 320°. What is each of the other two angles? (a) 20° (b) 40° (c) 160° (d) 21°
  2. 2.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) 165° (c) 195° (d) 15°
  3. 3.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 50° (b) 130° (c) 40° (d) 310°
  4. 4.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) 60° (c) 300° (d) 30°
  5. 5.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 65° (c) 130° (d) 155°
  6. 6.Two angles of a triangle are 60° and 75°. What is the third angle? (a) 105° (b) 45° (c) 120° (d) 135°
  7. 7.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 115° (b) 40° (c) 105° (d) 140°
  8. 8.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 225° (b) 46° (c) 45° (d) 135°
  9. 9.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 61° (b) 120° (c) 60° (d) 240°
  10. 10.Two angles of a triangle are 30° and 95°. What is the exterior angle at the third corner? (a) 150° (b) 85° (c) 125° (d) 55°
  11. 11.Two angles of a triangle are 40° and 55°. What is the exterior angle at the third corner? (a) 95° (b) 125° (c) 85° (d) 140°
  12. 12.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 75° (b) 145° (c) 110° (d) 105°
  13. 13.Two angles of a triangle are 35° and 85°. What is the third angle? (a) 60° (b) 95° (c) 120° (d) 145°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 70° (c) 20° (d) 55°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 165° (b) 30° (c) 15° (d) 16°
  16. 16.Two angles of a triangle are 25° and 30°. What is the exterior angle at the third corner? (a) 155° (b) 125° (c) 55° (d) 150°
  17. 17.Two angles of a triangle are 65° and 90°. What is the third angle? (a) 155° (b) 90° (c) 115° (d) 25°
  18. 18.Two angles of a triangle are 55° and 30°. What is the exterior angle at the third corner? (a) 85° (b) 125° (c) 95° (d) 150°
  19. 19.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 20° (b) 320° (c) 160° (d) 140°
  20. 20.Two angles of a triangle are 25° and 110°. What is the third angle? (a) 135° (b) 155° (c) 45° (d) 70°
  21. 21.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 310° (b) 155° (c) 130° (d) 25°
  22. 22.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 105° (b) 155° (c) 100° (d) 25°
  23. 23.Two angles of a triangle are 60° and 60°. What is the third angle? (a) 240° (b) 60° (c) 120° (d) 61°
  24. 24.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 110° (b) 90° (c) 160° (d) 270°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 100° (c) 50° (d) 80°
  26. 26.Two angles of a triangle are 20° and 115°. What is the third angle? (a) 135° (b) 160° (c) 65° (d) 45°
  27. 27.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 70° (b) 35° (c) 145° (d) 36°
  28. 28.Two angles of a triangle are 50° and 100°. What is the third angle? (a) 130° (b) 150° (c) 80° (d) 30°
  29. 29.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 40° (c) 50° (d) 140°
  30. 30.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 135° (b) 110° (c) 115° (d) 70°
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 135° (b) 270° (c) 45° (d) 90°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 120° (b) 30° (c) 40° (d) 60°
  33. 33.Two angles of a triangle are 55° and 110°. What is the third angle? (a) 165° (b) 125° (c) 70° (d) 15°
  34. 34.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 110° (b) 145° (c) 105° (d) 70°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 20° (c) 80° (d) 70°
  36. 36.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 130° (c) 25° (d) 50°
  37. 37.Two angles of a triangle are 30° and 20°. What is the exterior angle at the third corner? (a) 130° (b) 150° (c) 160° (d) 50°
  38. 38.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 120° (b) 150° (c) 30° (d) 90°
  39. 39.Two angles of a triangle are 30° and 90°. What is the third angle? (a) 120° (b) 150° (c) 90° (d) 60°
  40. 40.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 105° (b) 160° (c) 95° (d) 85°

Answer key

  1. 20°
  2. 15°
  3. 130°
  4. 120°
  5. 130°
  6. 45°
  7. 40°
  8. 45°
  9. 60°
  10. 125°
  11. 95°
  12. 105°
  13. 60°
  14. 55°
  15. 15°
  16. 55°
  17. 25°
  18. 85°
  19. 160°
  20. 45°
  21. 155°
  22. 25°
  23. 60°
  24. 90°
  25. 40°
  26. 45°
  27. 35°
  28. 30°
  29. 70°
  30. 70°
  31. 135°
  32. 30°
  33. 15°
  34. 70°
  35. 80°
  36. 25°
  37. 50°
  38. 150°
  39. 60°
  40. 95°

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