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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 131 · 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 two equal angles are 65° each. What is the third angle? (a) 65° (b) 50° (c) 25° (d) 115°
  2. 2.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) 340° (d) 160°
  3. 3.Two angles of a triangle are 25° and 125°. What is the exterior angle at the third corner? (a) 55° (b) 155° (c) 30° (d) 150°
  4. 4.Two angles of a triangle are 40° and 110°. What is the third angle? (a) 140° (b) 150° (c) 70° (d) 30°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 90° (c) 45° (d) 55°
  6. 6.Two angles of a triangle are 75° and 80°. What is the third angle? (a) 105° (b) 25° (c) 155° (d) 100°
  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) 140° (b) 320° (c) 50° (d) 40°
  8. 8.Two angles of a triangle are 30° and 70°. What is the third angle? (a) 110° (b) 150° (c) 80° (d) 100°
  9. 9.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 80° (c) 40° (d) 50°
  10. 10.Two angles of a triangle are 45° and 30°. What is the third angle? (a) 135° (b) 150° (c) 75° (d) 105°
  11. 11.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 80° (c) 100° (d) 50°
  12. 12.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 105° (b) 85° (c) 160° (d) 95°
  13. 13.Two angles of a triangle are 55° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 80° (c) 125° (d) 100°
  14. 14.Two angles of a triangle are 40° and 65°. What is the third angle? (a) 75° (b) 115° (c) 140° (d) 105°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 70° (b) 55° (c) 20° (d) 110°
  16. 16.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 165° (b) 16° (c) 195° (d) 15°
  17. 17.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 90° (b) 270° (c) 160° (d) 110°
  18. 18.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 165° (b) 105° (c) 90° (d) 15°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 50° (c) 80° (d) 100°
  20. 20.Two angles of a triangle are 55° and 90°. What is the third angle? (a) 145° (b) 35° (c) 90° (d) 125°
  21. 21.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 150° (d) 130°
  22. 22.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 150° (b) 95° (c) 115° (d) 85°
  23. 23.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) 60° (d) 300°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 55° (b) 70° (c) 250° (d) 125°
  25. 25.Two angles of a triangle are 25° and 80°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 155° (d) 100°
  26. 26.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 300° (b) 150° (c) 30° (d) 120°
  27. 27.Two angles of a triangle are 80° and 60°. What is the third angle? (a) 100° (b) 140° (c) 120° (d) 40°
  28. 28.Two angles of a triangle are 80° and 90°. What is the third angle? (a) 10° (b) 170° (c) 90° (d) 100°
  29. 29.Two angles of a triangle are 20° and 100°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 160° (d) 80°
  30. 30.Two angles of a triangle are 60° and 55°. What is the exterior angle at the third corner? (a) 115° (b) 120° (c) 65° (d) 125°
  31. 31.Two angles of a triangle are 60° and 60°. What is the third angle? (a) 240° (b) 120° (c) 61° (d) 60°
  32. 32.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 100° (b) 80° (c) 135° (d) 125°
  33. 33.Two angles of a triangle are 35° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 100° (c) 145° (d) 80°
  34. 34.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 35° (c) 145° (d) 110°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 40° (b) 20° (c) 21° (d) 160°
  36. 36.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 100° (c) 75° (d) 155°
  37. 37.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 55° (c) 35° (d) 70°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 95° (c) 170° (d) 86°
  39. 39.Two angles of a triangle are 20° and 45°. What is the exterior angle at the third corner? (a) 65° (b) 135° (c) 160° (d) 115°
  40. 40.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 60° (b) 125° (c) 115° (d) 120°

Answer key

  1. 50°
  2. 160°
  3. 150°
  4. 30°
  5. 45°
  6. 25°
  7. 140°
  8. 80°
  9. 80°
  10. 105°
  11. 40°
  12. 85°
  13. 80°
  14. 75°
  15. 55°
  16. 15°
  17. 90°
  18. 15°
  19. 50°
  20. 35°
  21. 80°
  22. 85°
  23. 120°
  24. 125°
  25. 105°
  26. 150°
  27. 40°
  28. 10°
  29. 120°
  30. 115°
  31. 60°
  32. 80°
  33. 80°
  34. 110°
  35. 20°
  36. 105°
  37. 70°
  38. 85°
  39. 65°
  40. 60°

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