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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 32 · 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 30° and 95°. What is the third angle? (a) 85° (b) 55° (c) 125° (d) 150°
  2. 2.Two angles of a triangle are 25° and 80°. What is the third angle? (a) 100° (b) 75° (c) 105° (d) 155°
  3. 3.Two angles of a triangle are 20° and 130°. What is the third angle? (a) 160° (b) 30° (c) 50° (d) 150°
  4. 4.Two angles of a triangle are 35° and 130°. What is the third angle? (a) 165° (b) 50° (c) 15° (d) 145°
  5. 5.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) 20° (d) 140°
  6. 6.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 135° (c) 45° (d) 91°
  7. 7.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 120° (c) 30° (d) 61°
  8. 8.Two angles of a triangle are 70° and 45°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 135° (d) 110°
  9. 9.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 130° (b) 155° (c) 105° (d) 75°
  10. 10.Two angles of a triangle are 80° and 60°. What is the third angle? (a) 40° (b) 120° (c) 100° (d) 140°
  11. 11.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 35° (b) 305° (c) 55° (d) 125°
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 140° (b) 70° (c) 71° (d) 110°
  13. 13.Two angles of a triangle are 70° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 220° (c) 40° (d) 140°
  14. 14.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°
  15. 15.Two angles of a triangle are 45° and 110°. What is the third angle? (a) 70° (b) 25° (c) 135° (d) 155°
  16. 16.Two angles of a triangle are 30° and 85°. What is the third angle? (a) 150° (b) 65° (c) 115° (d) 95°
  17. 17.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 80° (c) 130° (d) 40°
  18. 18.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 100° (b) 25° (c) 155° (d) 105°
  19. 19.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) 130° (d) 25°
  20. 20.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°
  21. 21.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 70° (c) 110° (d) 40°
  22. 22.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 125° (b) 25° (c) 80° (d) 155°
  23. 23.Two angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 155° (b) 140° (c) 65° (d) 115°
  24. 24.Two angles of a triangle are 30° and 30°. What is the third angle? (a) 300° (b) 150° (c) 60° (d) 120°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 150° (c) 60° (d) 75°
  26. 26.Two angles of a triangle are 65° and 70°. What is the third angle? (a) 135° (b) 110° (c) 45° (d) 115°
  27. 27.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 110° (c) 105° (d) 75°
  28. 28.Two angles of a triangle are 20° and 95°. What is the exterior angle at the third corner? (a) 115° (b) 160° (c) 85° (d) 65°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 30° (b) 210° (c) 75° (d) 105°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 60° (b) 120° (c) 61° (d) 59°
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 85° (b) 10° (c) 190° (d) 95°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 100° (c) 40° (d) 50°
  33. 33.Two angles of a triangle are 20° and 20°. What is the exterior angle at the third corner? (a) 140° (b) 320° (c) 160° (d) 40°
  34. 34.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 75° (c) 105° (d) 30°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 45° (b) 90° (c) 135° (d) 46°
  36. 36.Two angles of a triangle are 45° and 75°. What is the third angle? (a) 105° (b) 120° (c) 60° (d) 135°
  37. 37.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 75° (b) 105° (c) 145° (d) 140°
  38. 38.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 55° (b) 130° (c) 105° (d) 125°
  39. 39.Two angles of a triangle are 70° and 100°. What is the third angle? (a) 80° (b) 170° (c) 10° (d) 110°
  40. 40.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 105° (b) 75° (c) 100° (d) 155°

Answer key

  1. 55°
  2. 75°
  3. 30°
  4. 15°
  5. 20°
  6. 90°
  7. 60°
  8. 115°
  9. 75°
  10. 40°
  11. 125°
  12. 70°
  13. 140°
  14. 105°
  15. 25°
  16. 65°
  17. 80°
  18. 25°
  19. 25°
  20. 85°
  21. 40°
  22. 25°
  23. 65°
  24. 120°
  25. 75°
  26. 45°
  27. 105°
  28. 115°
  29. 105°
  30. 60°
  31. 95°
  32. 40°
  33. 40°
  34. 30°
  35. 45°
  36. 60°
  37. 105°
  38. 55°
  39. 10°
  40. 75°

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