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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 437 · 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) 121° (c) 240° (d) 120°
  2. 2.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 155° (b) 165° (c) 40° (d) 15°
  3. 3.Two angles of a triangle are 60° and 20°. What is the third angle? (a) 80° (b) 160° (c) 120° (d) 100°
  4. 4.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 100° (b) 150° (c) 110° (d) 30°
  5. 5.Two angles of a triangle are 50° and 55°. What is the third angle? (a) 75° (b) 105° (c) 125° (d) 130°
  6. 6.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 110° (c) 35° (d) 145°
  7. 7.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 40° (b) 320° (c) 140° (d) 50°
  8. 8.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 100° (c) 20° (d) 80°
  9. 9.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 130° (c) 80° (d) 50°
  10. 10.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 115° (b) 150° (c) 85° (d) 95°
  11. 11.Two angles of a triangle are 70° and 70°. What is the third angle? (a) 220° (b) 110° (c) 40° (d) 140°
  12. 12.Two angles of a triangle are 70° and 65°. What is the third angle? (a) 115° (b) 45° (c) 110° (d) 135°
  13. 13.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 55° (c) 70° (d) 35°
  14. 14.Two angles of a triangle are 50° and 25°. What is the third angle? (a) 75° (b) 155° (c) 130° (d) 105°
  15. 15.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 60° (b) 120° (c) 30° (d) 300°
  16. 16.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 125° (b) 35° (c) 305° (d) 55°
  17. 17.Two angles of a triangle are 40° and 110°. What is the exterior angle at the third corner? (a) 30° (b) 70° (c) 140° (d) 150°
  18. 18.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 95° (b) 130° (c) 85° (d) 145°
  19. 19.Two angles of a triangle are 60° and 100°. What is the third angle? (a) 120° (b) 20° (c) 80° (d) 160°
  20. 20.Two angles of a triangle are 65° and 100°. What is the third angle? (a) 165° (b) 115° (c) 15° (d) 80°
  21. 21.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 11° (c) 160° (d) 10°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 66° (b) 115° (c) 65° (d) 130°
  23. 23.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 50° (c) 65° (d) 130°
  24. 24.Two angles of a triangle are 40° and 75°. What is the third angle? (a) 115° (b) 65° (c) 105° (d) 140°
  25. 25.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 61° (b) 240° (c) 60° (d) 120°
  26. 26.Two angles of a triangle are 45° and 125°. What is the third angle? (a) 10° (b) 170° (c) 135° (d) 55°
  27. 27.Two angles of a triangle are 45° and 70°. What is the third angle? (a) 135° (b) 115° (c) 65° (d) 110°
  28. 28.Two angles of a triangle are 25° and 55°. What is the third angle? (a) 80° (b) 125° (c) 155° (d) 100°
  29. 29.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 60° (c) 70° (d) 30°
  30. 30.Two angles of a triangle are 65° and 85°. What is the third angle? (a) 115° (b) 150° (c) 30° (d) 95°
  31. 31.Two angles of a triangle are 45° and 25°. What is the third angle? (a) 135° (b) 110° (c) 155° (d) 70°
  32. 32.Two angles of a triangle are 50° and 80°. What is the exterior angle at the third corner? (a) 130° (b) 100° (c) 230° (d) 50°
  33. 33.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 145° (b) 215° (c) 35° (d) 36°
  34. 34.Two angles of a triangle are 70° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 35° (c) 145° (d) 110°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 46° (c) 90° (d) 45°
  36. 36.Two angles of a triangle are 35° and 50°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 145° (d) 130°
  37. 37.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 115° (b) 45° (c) 110° (d) 135°
  38. 38.Two angles of a triangle are 35° and 60°. What is the third angle? (a) 95° (b) 85° (c) 120° (d) 145°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 59° (b) 61° (c) 120° (d) 60°
  40. 40.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 115° (b) 105° (c) 65° (d) 140°

Answer key

  1. 120°
  2. 15°
  3. 100°
  4. 150°
  5. 75°
  6. 110°
  7. 140°
  8. 20°
  9. 80°
  10. 85°
  11. 40°
  12. 45°
  13. 70°
  14. 105°
  15. 120°
  16. 125°
  17. 150°
  18. 95°
  19. 20°
  20. 15°
  21. 10°
  22. 65°
  23. 65°
  24. 65°
  25. 60°
  26. 10°
  27. 65°
  28. 100°
  29. 60°
  30. 30°
  31. 110°
  32. 130°
  33. 35°
  34. 145°
  35. 45°
  36. 85°
  37. 135°
  38. 85°
  39. 60°
  40. 65°

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