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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 202 · 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 30° and 30°. What is the third angle? (a) 150° (b) 60° (c) 300° (d) 120°
  2. 2.Two angles of a triangle are 55° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 30° (c) 150° (d) 125°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 40° (c) 140° (d) 50°
  4. 4.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 51° (b) 50° (c) 230° (d) 130°
  5. 5.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 115° (b) 140° (c) 105° (d) 40°
  6. 6.Two angles of a triangle are 45° and 45°. What is the third angle? (a) 270° (b) 91° (c) 90° (d) 135°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 61° (b) 60° (c) 59° (d) 120°
  8. 8.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 40° (b) 140° (c) 105° (d) 115°
  9. 9.Two angles of a triangle are 35° and 120°. What is the third angle? (a) 60° (b) 155° (c) 145° (d) 25°
  10. 10.Two angles of a triangle are 55° and 75°. What is the exterior angle at the third corner? (a) 125° (b) 105° (c) 130° (d) 50°
  11. 11.Two angles of a triangle are 35° and 95°. What is the third angle? (a) 145° (b) 130° (c) 85° (d) 50°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 30° (c) 20° (d) 40°
  13. 13.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 160° (b) 40° (c) 21° (d) 20°
  14. 14.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°
  15. 15.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 280° (b) 140° (c) 80° (d) 100°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 25° (b) 26° (c) 50° (d) 155°
  17. 17.Two angles of a triangle are 40° and 95°. What is the third angle? (a) 140° (b) 135° (c) 85° (d) 45°
  18. 18.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 70° (b) 35° (c) 55° (d) 125°
  19. 19.Two angles of a triangle are 50° and 55°. What is the exterior angle at the third corner? (a) 75° (b) 130° (c) 105° (d) 125°
  20. 20.Two angles of a triangle are 50° and 20°. What is the third angle? (a) 160° (b) 110° (c) 70° (d) 130°
  21. 21.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 15° (c) 30° (d) 105°
  22. 22.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 40° (b) 15° (c) 155° (d) 165°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 11° (b) 10° (c) 20° (d) 170°
  24. 24.Two angles of a triangle are 55° and 65°. What is the exterior angle at the third corner? (a) 120° (b) 60° (c) 115° (d) 125°
  25. 25.Two angles of a triangle are 50° and 95°. What is the third angle? (a) 35° (b) 145° (c) 130° (d) 85°
  26. 26.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 75° (b) 155° (c) 130° (d) 105°
  27. 27.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 35° (b) 215° (c) 145° (d) 36°
  28. 28.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) 105° (c) 15° (d) 75°
  29. 29.Two angles of a triangle are 70° and 85°. What is the third angle? (a) 95° (b) 25° (c) 110° (d) 155°
  30. 30.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 100° (c) 140° (d) 40°
  31. 31.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 105° (b) 80° (c) 100° (d) 155°
  32. 32.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) 76° (c) 105° (d) 75°
  33. 33.Two angles of a triangle are 75° and 65°. What is the exterior angle at the third corner? (a) 40° (b) 105° (c) 115° (d) 140°
  34. 34.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 20° (b) 100° (c) 80° (d) 10°
  35. 35.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 140° (b) 110° (c) 250° (d) 70°
  36. 36.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 15° (b) 195° (c) 165° (d) 16°
  37. 37.Two angles of a triangle are 20° and 85°. What is the exterior angle at the third corner? (a) 75° (b) 95° (c) 160° (d) 105°
  38. 38.Two angles of a triangle are 70° and 25°. What is the third angle? (a) 85° (b) 155° (c) 110° (d) 95°
  39. 39.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 85° (c) 10° (d) 5°
  40. 40.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 95° (b) 140° (c) 135° (d) 85°

Answer key

  1. 120°
  2. 150°
  3. 70°
  4. 50°
  5. 40°
  6. 90°
  7. 60°
  8. 140°
  9. 25°
  10. 130°
  11. 50°
  12. 20°
  13. 20°
  14. 30°
  15. 100°
  16. 25°
  17. 45°
  18. 70°
  19. 105°
  20. 110°
  21. 30°
  22. 15°
  23. 10°
  24. 120°
  25. 35°
  26. 75°
  27. 35°
  28. 105°
  29. 25°
  30. 100°
  31. 80°
  32. 75°
  33. 140°
  34. 20°
  35. 70°
  36. 15°
  37. 105°
  38. 85°
  39. 10°
  40. 85°

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