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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 121 · 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.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 40° (c) 50° (d) 80°
  2. 2.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 25° (c) 155° (d) 130°
  3. 3.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) 30° (c) 300° (d) 60°
  4. 4.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 5° (b) 95° (c) 85° (d) 275°
  5. 5.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 75° (b) 140° (c) 145° (d) 105°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 65° (b) 50° (c) 230° (d) 115°
  7. 7.Two angles of a triangle are 40° and 120°. What is the third angle? (a) 60° (b) 140° (c) 160° (d) 20°
  8. 8.Two angles of a triangle are 25° and 115°. What is the exterior angle at the third corner? (a) 140° (b) 40° (c) 65° (d) 155°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 100° (c) 80° (d) 10°
  10. 10.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 60° (b) 120° (c) 40° (d) 30°
  11. 11.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 56° (b) 235° (c) 125° (d) 55°
  12. 12.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 10° (c) 80° (d) 20°
  13. 13.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 135° (b) 125° (c) 45° (d) 100°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 60° (b) 150° (c) 31° (d) 30°
  15. 15.Two angles of a triangle are 55° and 30°. What is the third angle? (a) 85° (b) 125° (c) 95° (d) 150°
  16. 16.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 145° (b) 105° (c) 110° (d) 70°
  17. 17.Two angles of a triangle are 55° and 25°. What is the third angle? (a) 80° (b) 155° (c) 125° (d) 100°
  18. 18.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 20° (c) 11° (d) 10°
  19. 19.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 145° (b) 155° (c) 60° (d) 120°
  20. 20.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 150° (b) 145° (c) 65° (d) 115°
  21. 21.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 71° (b) 110° (c) 140° (d) 70°
  22. 22.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) 55° (c) 325° (d) 145°
  23. 23.Two angles of a triangle are 50° and 25°. What is the third angle? (a) 130° (b) 105° (c) 75° (d) 155°
  24. 24.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 90° (b) 15° (c) 105° (d) 165°
  25. 25.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 150° (b) 70° (c) 100° (d) 110°
  26. 26.Two angles of a triangle are 60° and 45°. What is the exterior angle at the third corner? (a) 75° (b) 120° (c) 135° (d) 105°
  27. 27.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 115° (c) 65° (d) 50°
  28. 28.Two angles of a triangle are 45° and 120°. What is the third angle? (a) 165° (b) 15° (c) 135° (d) 60°
  29. 29.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 50° (b) 40° (c) 140° (d) 320°
  30. 30.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 135° (b) 45° (c) 46° (d) 225°
  31. 31.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 110° (c) 70° (d) 290°
  32. 32.Two angles of a triangle are 35° and 45°. What is the exterior angle at the third corner? (a) 145° (b) 100° (c) 135° (d) 80°
  33. 33.Two angles of a triangle are 75° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 140° (c) 105° (d) 40°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 20° (b) 140° (c) 320° (d) 160°
  35. 35.Two angles of a triangle are 20° and 20°. What is the third angle? (a) 40° (b) 320° (c) 140° (d) 160°
  36. 36.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 70° (c) 20° (d) 80°
  37. 37.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 80° (b) 120° (c) 140° (d) 100°
  38. 38.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 120° (b) 145° (c) 95° (d) 85°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 70° (b) 125° (c) 250° (d) 55°
  40. 40.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 70° (c) 30° (d) 60°

Answer key

  1. 40°
  2. 130°
  3. 120°
  4. 95°
  5. 75°
  6. 115°
  7. 20°
  8. 140°
  9. 50°
  10. 30°
  11. 55°
  12. 20°
  13. 45°
  14. 30°
  15. 95°
  16. 70°
  17. 100°
  18. 10°
  19. 60°
  20. 65°
  21. 70°
  22. 145°
  23. 105°
  24. 15°
  25. 70°
  26. 105°
  27. 50°
  28. 15°
  29. 140°
  30. 45°
  31. 70°
  32. 80°
  33. 140°
  34. 160°
  35. 140°
  36. 80°
  37. 100°
  38. 95°
  39. 125°
  40. 60°

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