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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 489 · 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 40° and 45°. What is the exterior angle at the third corner? (a) 95° (b) 135° (c) 85° (d) 140°
  2. 2.Two angles of a triangle are 50° and 55°. What is the third angle? (a) 130° (b) 125° (c) 75° (d) 105°
  3. 3.Two angles of a triangle are 30° and 90°. What is the third angle? (a) 150° (b) 90° (c) 120° (d) 60°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 200° (b) 80° (c) 20° (d) 100°
  5. 5.Two angles of a triangle are 50° and 75°. What is the third angle? (a) 55° (b) 125° (c) 130° (d) 105°
  6. 6.Two angles of a triangle are 60° and 55°. What is the third angle? (a) 65° (b) 120° (c) 125° (d) 115°
  7. 7.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 15° (c) 30° (d) 105°
  8. 8.Two angles of a triangle are 20° and 55°. What is the third angle? (a) 125° (b) 105° (c) 75° (d) 160°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 100° (b) 40° (c) 140° (d) 280°
  10. 10.Two angles of a triangle are 30° and 110°. What is the exterior angle at the third corner? (a) 70° (b) 40° (c) 150° (d) 140°
  11. 11.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 110° (c) 35° (d) 55°
  12. 12.Two angles of a triangle are 45° and 120°. What is the third angle? (a) 60° (b) 15° (c) 165° (d) 135°
  13. 13.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) 125° (d) 55°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 50° (c) 80° (d) 40°
  15. 15.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 75° (b) 110° (c) 145° (d) 105°
  16. 16.Two angles of a triangle are 40° and 75°. What is the third angle? (a) 115° (b) 65° (c) 105° (d) 140°
  17. 17.Two angles of a triangle are 30° and 35°. What is the third angle? (a) 65° (b) 150° (c) 115° (d) 145°
  18. 18.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 40° (c) 50° (d) 140°
  19. 19.Two angles of a triangle are 50° and 40°. What is the third angle? (a) 270° (b) 90° (c) 140° (d) 130°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 110° (b) 140° (c) 70° (d) 71°
  21. 21.Two angles of a triangle are 35° and 90°. What is the third angle? (a) 145° (b) 55° (c) 125° (d) 90°
  22. 22.Two angles of a triangle are 60° and 55°. What is the exterior angle at the third corner? (a) 65° (b) 125° (c) 115° (d) 120°
  23. 23.Two angles of a triangle are 25° and 125°. What is the exterior angle at the third corner? (a) 55° (b) 150° (c) 155° (d) 30°
  24. 24.Two angles of a triangle are 60° and 25°. What is the exterior angle at the third corner? (a) 95° (b) 120° (c) 155° (d) 85°
  25. 25.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 100° (c) 10° (d) 20°
  26. 26.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 110° (b) 56° (c) 125° (d) 55°
  27. 27.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 110° (b) 70° (c) 145° (d) 290°
  28. 28.Two angles of a triangle are 60° and 85°. What is the third angle? (a) 95° (b) 35° (c) 120° (d) 145°
  29. 29.Two angles of a triangle are 40° and 25°. What is the third angle? (a) 65° (b) 140° (c) 115° (d) 155°
  30. 30.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 125° (b) 235° (c) 55° (d) 56°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 80° (b) 160° (c) 20° (d) 70°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 80° (c) 50° (d) 100°
  33. 33.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 30° (b) 120° (c) 300° (d) 60°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 150° (b) 31° (c) 60° (d) 30°
  35. 35.Two angles of a triangle are 30° and 75°. What is the third angle? (a) 150° (b) 255° (c) 105° (d) 75°
  36. 36.Two angles of a triangle are 80° and 90°. What is the third angle? (a) 90° (b) 10° (c) 100° (d) 170°
  37. 37.Two angles of a triangle are 60° and 70°. What is the exterior angle at the third corner? (a) 120° (b) 110° (c) 50° (d) 130°
  38. 38.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 205° (b) 25° (c) 155° (d) 26°
  39. 39.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 70° (c) 40° (d) 50°
  40. 40.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 135° (b) 80° (c) 145° (d) 100°

Answer key

  1. 85°
  2. 75°
  3. 60°
  4. 100°
  5. 55°
  6. 65°
  7. 30°
  8. 105°
  9. 140°
  10. 140°
  11. 110°
  12. 15°
  13. 125°
  14. 40°
  15. 75°
  16. 65°
  17. 115°
  18. 100°
  19. 90°
  20. 70°
  21. 55°
  22. 115°
  23. 150°
  24. 85°
  25. 20°
  26. 55°
  27. 110°
  28. 35°
  29. 115°
  30. 55°
  31. 80°
  32. 50°
  33. 120°
  34. 30°
  35. 75°
  36. 10°
  37. 130°
  38. 25°
  39. 70°
  40. 100°

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