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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 383 · 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 130°. What is the third angle? (a) 160° (b) 150° (c) 30° (d) 50°
  2. 2.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 200° (b) 160° (c) 20° (d) 21°
  3. 3.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 80° (b) 155° (c) 100° (d) 105°
  4. 4.Two angles of a triangle are 35° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 135° (c) 145° (d) 45°
  5. 5.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 150° (b) 30° (c) 210° (d) 31°
  6. 6.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 55° (b) 70° (c) 110° (d) 20°
  7. 7.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 80° (b) 105° (c) 155° (d) 100°
  8. 8.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 220° (b) 40° (c) 140° (d) 41°
  9. 9.Two angles of a triangle are 45° and 60°. What is the third angle? (a) 120° (b) 135° (c) 75° (d) 105°
  10. 10.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 86° (c) 85° (d) 95°
  11. 11.Two angles of a triangle are 65° and 30°. What is the exterior angle at the third corner? (a) 85° (b) 150° (c) 95° (d) 115°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 70° (c) 160° (d) 80°
  13. 13.Two angles of a triangle are 35° and 70°. What is the third angle? (a) 105° (b) 110° (c) 75° (d) 145°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 170° (b) 20° (c) 11° (d) 10°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 86° (c) 170° (d) 85°
  16. 16.Two angles of a triangle are 25° and 60°. What is the exterior angle at the third corner? (a) 155° (b) 85° (c) 120° (d) 95°
  17. 17.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 30° (b) 165° (c) 15° (d) 16°
  18. 18.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 60° (c) 30° (d) 61°
  19. 19.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°
  20. 20.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 30° (b) 105° (c) 75° (d) 15°
  21. 21.Two angles of a triangle are 60° and 20°. What is the exterior angle at the third corner? (a) 120° (b) 100° (c) 80° (d) 160°
  22. 22.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 145° (c) 35° (d) 55°
  23. 23.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 71° (b) 70° (c) 110° (d) 250°
  24. 24.Two angles of a triangle are 20° and 120°. What is the exterior angle at the third corner? (a) 40° (b) 140° (c) 60° (d) 160°
  25. 25.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 130° (b) 105° (c) 155° (d) 75°
  26. 26.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 50° (c) 230° (d) 130°
  27. 27.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 235° (d) 110°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 21° (b) 160° (c) 40° (d) 20°
  29. 29.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 100° (b) 40° (c) 120° (d) 140°
  30. 30.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 25° (b) 155° (c) 65° (d) 335°
  31. 31.Two angles of a triangle are 30° and 30°. What is the third angle? (a) 150° (b) 300° (c) 120° (d) 60°
  32. 32.Two angles of a triangle are 70° and 100°. What is the third angle? (a) 110° (b) 80° (c) 10° (d) 170°
  33. 33.Two angles of a triangle are 45° and 85°. What is the third angle? (a) 135° (b) 95° (c) 130° (d) 50°
  34. 34.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 136° (b) 315° (c) 135° (d) 45°
  35. 35.Two angles of a triangle are 30° and 120°. What is the third angle? (a) 30° (b) 210° (c) 60° (d) 150°
  36. 36.Two angles of a triangle are 45° and 45°. What is the third angle? (a) 135° (b) 91° (c) 90° (d) 270°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 40° (c) 50° (d) 130°
  38. 38.Two angles of a triangle are 35° and 65°. What is the third angle? (a) 80° (b) 100° (c) 145° (d) 115°
  39. 39.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 115° (b) 100° (c) 145° (d) 65°
  40. 40.Two angles of a triangle are 55° and 75°. What is the exterior angle at the third corner? (a) 125° (b) 130° (c) 50° (d) 105°

Answer key

  1. 30°
  2. 20°
  3. 80°
  4. 135°
  5. 30°
  6. 55°
  7. 100°
  8. 40°
  9. 75°
  10. 85°
  11. 95°
  12. 80°
  13. 75°
  14. 10°
  15. 85°
  16. 85°
  17. 15°
  18. 60°
  19. 120°
  20. 30°
  21. 80°
  22. 110°
  23. 70°
  24. 140°
  25. 75°
  26. 130°
  27. 125°
  28. 20°
  29. 140°
  30. 155°
  31. 120°
  32. 10°
  33. 50°
  34. 135°
  35. 30°
  36. 90°
  37. 65°
  38. 80°
  39. 65°
  40. 130°

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