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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 407 · 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 straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 60° (b) 240° (c) 121° (d) 120°
  2. 2.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 320° (b) 20° (c) 160° (d) 140°
  3. 3.Two angles of a triangle are 20° and 125°. What is the exterior angle at the third corner? (a) 55° (b) 35° (c) 145° (d) 160°
  4. 4.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 240° (b) 120° (c) 60° (d) 61°
  5. 5.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 70° (c) 160° (d) 340°
  6. 6.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 140° (b) 40° (c) 50° (d) 320°
  7. 7.Two angles of a triangle are 50° and 50°. What is the exterior angle at the third corner? (a) 260° (b) 80° (c) 100° (d) 130°
  8. 8.Two angles of a triangle are 30° and 50°. What is the third angle? (a) 100° (b) 150° (c) 80° (d) 130°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 55° (b) 20° (c) 110° (d) 70°
  10. 10.Two angles of a triangle are 25° and 115°. What is the exterior angle at the third corner? (a) 155° (b) 140° (c) 65° (d) 40°
  11. 11.Two angles of a triangle are 35° and 60°. What is the third angle? (a) 85° (b) 145° (c) 95° (d) 120°
  12. 12.Two angles of a triangle are 55° and 70°. What is the exterior angle at the third corner? (a) 235° (b) 55° (c) 125° (d) 110°
  13. 13.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 115° (b) 95° (c) 30° (d) 150°
  14. 14.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 290° (b) 110° (c) 145° (d) 70°
  15. 15.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 50° (c) 115° (d) 25°
  16. 16.Two angles of a triangle are 55° and 30°. What is the third angle? (a) 85° (b) 125° (c) 95° (d) 150°
  17. 17.Two angles of a triangle are 75° and 30°. What is the third angle? (a) 105° (b) 75° (c) 255° (d) 150°
  18. 18.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) 100° (d) 50°
  19. 19.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 230° (b) 130° (c) 50° (d) 51°
  20. 20.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) 60° (d) 30°
  21. 21.Two angles of a triangle are 55° and 50°. What is the third angle? (a) 75° (b) 130° (c) 125° (d) 105°
  22. 22.Two angles of a triangle are 70° and 65°. What is the third angle? (a) 110° (b) 115° (c) 135° (d) 45°
  23. 23.Two angles of a triangle are 50° and 85°. What is the exterior angle at the third corner? (a) 45° (b) 130° (c) 95° (d) 135°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 30° (b) 16° (c) 165° (d) 15°
  25. 25.Two angles of a triangle are 20° and 120°. What is the third angle? (a) 40° (b) 60° (c) 160° (d) 140°
  26. 26.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 110° (c) 45° (d) 35°
  27. 27.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 115° (b) 65° (c) 245° (d) 66°
  28. 28.Two angles of a triangle are 65° and 75°. What is the third angle? (a) 40° (b) 140° (c) 115° (d) 105°
  29. 29.Two angles of a triangle are 35° and 100°. What is the exterior angle at the third corner? (a) 145° (b) 80° (c) 45° (d) 135°
  30. 30.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 15° (b) 165° (c) 155° (d) 40°
  31. 31.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 325° (b) 55° (c) 145° (d) 35°
  32. 32.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 80° (b) 155° (c) 105° (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 angles of a triangle are 20° and 115°. What is the third angle? (a) 45° (b) 65° (c) 135° (d) 160°
  35. 35.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 120° (c) 30° (d) 61°
  36. 36.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 100° (b) 35° (c) 115° (d) 145°
  37. 37.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 65° (b) 155° (c) 25° (d) 335°
  38. 38.Two angles of a triangle are 25° and 90°. What is the exterior angle at the third corner? (a) 155° (b) 90° (c) 65° (d) 115°
  39. 39.Two angles of a triangle are 25° and 85°. What is the third angle? (a) 155° (b) 70° (c) 95° (d) 110°
  40. 40.Two angles of a triangle are 50° and 50°. What is the third angle? (a) 260° (b) 130° (c) 80° (d) 100°

Answer key

  1. 120°
  2. 160°
  3. 145°
  4. 60°
  5. 160°
  6. 140°
  7. 100°
  8. 100°
  9. 55°
  10. 140°
  11. 85°
  12. 125°
  13. 150°
  14. 110°
  15. 50°
  16. 95°
  17. 75°
  18. 50°
  19. 50°
  20. 60°
  21. 75°
  22. 45°
  23. 135°
  24. 15°
  25. 40°
  26. 35°
  27. 65°
  28. 40°
  29. 135°
  30. 15°
  31. 145°
  32. 100°
  33. 120°
  34. 45°
  35. 60°
  36. 35°
  37. 155°
  38. 115°
  39. 70°
  40. 80°

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