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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 817 · 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 130°. What is the third angle? (a) 140° (b) 170° (c) 10° (d) 50°
  2. 2.Two angles of a triangle are 75° and 45°. What is the exterior angle at the third corner? (a) 60° (b) 105° (c) 120° (d) 135°
  3. 3.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 100° (b) 75° (c) 155° (d) 105°
  4. 4.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 100° (b) 150° (c) 110° (d) 80°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 50° (c) 10° (d) 80°
  6. 6.Two angles of a triangle are 65° and 25°. What is the third angle? (a) 155° (b) 270° (c) 90° (d) 115°
  7. 7.Two angles of a triangle are 80° and 50°. What is the third angle? (a) 130° (b) 230° (c) 100° (d) 50°
  8. 8.Two angles of a triangle are 20° and 25°. What is the exterior angle at the third corner? (a) 135° (b) 45° (c) 155° (d) 160°
  9. 9.Two angles of a triangle are 75° and 60°. What is the exterior angle at the third corner? (a) 105° (b) 135° (c) 45° (d) 120°
  10. 10.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) 75° (c) 105° (d) 15°
  11. 11.Two angles of a triangle are 30° and 140°. What is the third angle? (a) 150° (b) 170° (c) 40° (d) 10°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 60° (c) 30° (d) 120°
  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) 55° (b) 305° (c) 125° (d) 35°
  14. 14.Two angles of a triangle are 35° and 105°. What is the exterior angle at the third corner? (a) 145° (b) 40° (c) 140° (d) 75°
  15. 15.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 155° (b) 26° (c) 25° (d) 205°
  16. 16.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 330° (b) 30° (c) 60° (d) 150°
  17. 17.Two angles of a triangle are 55° and 115°. What is the third angle? (a) 170° (b) 125° (c) 10° (d) 65°
  18. 18.Two angles of a triangle are 20° and 115°. What is the third angle? (a) 160° (b) 135° (c) 45° (d) 65°
  19. 19.Two angles of a triangle are 45° and 105°. What is the third angle? (a) 135° (b) 75° (c) 30° (d) 150°
  20. 20.Two angles of a triangle are 35° and 65°. What is the exterior angle at the third corner? (a) 100° (b) 145° (c) 115° (d) 80°
  21. 21.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 25° (b) 155° (c) 310° (d) 130°
  22. 22.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 270° (c) 90° (d) 145°
  23. 23.Two angles of a triangle are 50° and 105°. What is the third angle? (a) 75° (b) 155° (c) 130° (d) 25°
  24. 24.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 61° (c) 120° (d) 60°
  25. 25.Two angles of a triangle are 60° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 120° (c) 50° (d) 130°
  26. 26.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 56° (b) 55° (c) 125° (d) 110°
  27. 27.Two angles of a triangle are 20° and 70°. What is the exterior angle at the third corner? (a) 90° (b) 110° (c) 160° (d) 270°
  28. 28.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 60° (c) 70° (d) 120°
  29. 29.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 75° (c) 30° (d) 150°
  30. 30.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 255° (b) 75° (c) 105° (d) 76°
  31. 31.Two angles of a triangle are 70° and 75°. What is the third angle? (a) 145° (b) 35° (c) 110° (d) 105°
  32. 32.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 40° (c) 100° (d) 50°
  33. 33.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 100° (b) 35° (c) 115° (d) 145°
  34. 34.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 25° (c) 115° (d) 65°
  35. 35.Two angles of a triangle are 30° and 20°. What is the third angle? (a) 50° (b) 160° (c) 130° (d) 150°
  36. 36.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 30° (c) 15° (d) 75°
  37. 37.Two angles of a triangle are 20° and 55°. What is the third angle? (a) 160° (b) 75° (c) 125° (d) 105°
  38. 38.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 10° (b) 5° (c) 95° (d) 85°
  39. 39.Two angles of a triangle are 20° and 100°. What is the third angle? (a) 120° (b) 80° (c) 160° (d) 60°
  40. 40.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 45° (b) 95° (c) 130° (d) 135°

Answer key

  1. 10°
  2. 120°
  3. 75°
  4. 80°
  5. 50°
  6. 90°
  7. 50°
  8. 45°
  9. 135°
  10. 105°
  11. 10°
  12. 30°
  13. 125°
  14. 140°
  15. 25°
  16. 150°
  17. 10°
  18. 45°
  19. 30°
  20. 100°
  21. 155°
  22. 90°
  23. 25°
  24. 60°
  25. 130°
  26. 55°
  27. 90°
  28. 60°
  29. 75°
  30. 75°
  31. 35°
  32. 100°
  33. 35°
  34. 50°
  35. 130°
  36. 30°
  37. 105°
  38. 10°
  39. 60°
  40. 45°

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