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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 466 · 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 20° and 100°. What is the exterior angle at the third corner? (a) 60° (b) 80° (c) 160° (d) 120°
  2. 2.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 55° (b) 125° (c) 305° (d) 35°
  3. 3.Two angles of a triangle are 80° and 50°. What is the exterior angle at the third corner? (a) 100° (b) 130° (c) 50° (d) 230°
  4. 4.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 35° (b) 145° (c) 325° (d) 55°
  5. 5.Two angles of a triangle are 25° and 60°. What is the exterior angle at the third corner? (a) 85° (b) 120° (c) 95° (d) 155°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 120° (b) 61° (c) 59° (d) 60°
  7. 7.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 110° (b) 70° (c) 135° (d) 115°
  8. 8.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 65° (b) 145° (c) 115° (d) 100°
  9. 9.Two angles of a triangle are 40° and 80°. What is the third angle? (a) 100° (b) 60° (c) 140° (d) 120°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 135° (b) 46° (c) 45° (d) 90°
  11. 11.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 150° (b) 110° (c) 100° (d) 30°
  12. 12.Two angles of a triangle are 25° and 25°. What is the exterior angle at the third corner? (a) 310° (b) 130° (c) 155° (d) 50°
  13. 13.Two angles of a triangle are 55° and 110°. What is the third angle? (a) 15° (b) 70° (c) 165° (d) 125°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 60° (c) 30° (d) 120°
  15. 15.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 240° (b) 61° (c) 60° (d) 120°
  16. 16.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 85° (b) 275° (c) 5° (d) 95°
  17. 17.Two angles of a triangle are 55° and 30°. What is the third angle? (a) 150° (b) 85° (c) 95° (d) 125°
  18. 18.Two angles of a triangle are 50° and 75°. What is the third angle? (a) 130° (b) 55° (c) 125° (d) 105°
  19. 19.Two angles of a triangle are 55° and 50°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 125° (d) 130°
  20. 20.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 26° (b) 155° (c) 205° (d) 25°
  21. 21.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 60° (b) 31° (c) 30° (d) 150°
  22. 22.Two angles of a triangle are 20° and 45°. What is the third angle? (a) 135° (b) 65° (c) 160° (d) 115°
  23. 23.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 120° (b) 130° (c) 70° (d) 110°
  24. 24.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 270° (c) 115° (d) 90°
  25. 25.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 120° (b) 100° (c) 80° (d) 140°
  26. 26.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 130° (b) 310° (c) 40° (d) 50°
  27. 27.Two angles of a triangle are 75° and 60°. What is the third angle? (a) 45° (b) 135° (c) 105° (d) 120°
  28. 28.Two angles of a triangle are 25° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 155° (c) 100° (d) 80°
  29. 29.Two angles of a triangle are 65° and 70°. What is the third angle? (a) 45° (b) 110° (c) 115° (d) 135°
  30. 30.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 30° (b) 105° (c) 75° (d) 15°
  31. 31.Two angles of a triangle are 50° and 70°. What is the exterior angle at the third corner? (a) 60° (b) 130° (c) 110° (d) 120°
  32. 32.Two angles of a triangle are 35° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 125° (c) 55° (d) 145°
  33. 33.Two angles of a triangle are 25° and 65°. What is the third angle? (a) 90° (b) 155° (c) 270° (d) 115°
  34. 34.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 250° (b) 71° (c) 70° (d) 110°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 125° (b) 250° (c) 55° (d) 70°
  36. 36.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 105° (b) 140° (c) 115° (d) 65°
  37. 37.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 95° (c) 86° (d) 265°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 35° (c) 25° (d) 50°
  39. 39.Two angles of a triangle are 40° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 120° (c) 140° (d) 60°
  40. 40.Two angles of a triangle are 45° and 40°. What is the third angle? (a) 140° (b) 95° (c) 135° (d) 85°

Answer key

  1. 120°
  2. 125°
  3. 130°
  4. 145°
  5. 85°
  6. 60°
  7. 70°
  8. 65°
  9. 60°
  10. 45°
  11. 150°
  12. 50°
  13. 15°
  14. 60°
  15. 60°
  16. 95°
  17. 95°
  18. 55°
  19. 105°
  20. 25°
  21. 30°
  22. 115°
  23. 70°
  24. 90°
  25. 80°
  26. 130°
  27. 45°
  28. 80°
  29. 45°
  30. 30°
  31. 120°
  32. 125°
  33. 90°
  34. 70°
  35. 125°
  36. 65°
  37. 85°
  38. 25°
  39. 60°
  40. 95°

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