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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 360 · 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 55° and 100°. What is the third angle? (a) 80° (b) 25° (c) 155° (d) 125°
  2. 2.Two angles of a triangle are 80° and 55°. What is the third angle? (a) 125° (b) 100° (c) 45° (d) 135°
  3. 3.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 20° (b) 160° (c) 21° (d) 200°
  4. 4.Two angles of a triangle are 25° and 30°. What is the third angle? (a) 150° (b) 155° (c) 55° (d) 125°
  5. 5.Two angles of a triangle are 45° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 45° (c) 225° (d) 135°
  6. 6.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 100° (c) 130° (d) 80°
  7. 7.Two angles of a triangle are 60° and 65°. What is the third angle? (a) 125° (b) 55° (c) 120° (d) 115°
  8. 8.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 105° (b) 30° (c) 210° (d) 75°
  9. 9.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 145° (c) 110° (d) 55°
  10. 10.Two angles of a triangle are 35° and 115°. What is the exterior angle at the third corner? (a) 145° (b) 65° (c) 30° (d) 150°
  11. 11.Two angles of a triangle are 50° and 50°. What is the exterior angle at the third corner? (a) 260° (b) 100° (c) 80° (d) 130°
  12. 12.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 50° (c) 100° (d) 40°
  13. 13.Two angles of a triangle are 55° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 55° (c) 125° (d) 235°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 50° (c) 80° (d) 40°
  15. 15.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 210° (b) 150° (c) 31° (d) 30°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 25° (c) 30° (d) 15°
  17. 17.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 61° (b) 120° (c) 59° (d) 60°
  18. 18.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 150° (b) 80° (c) 100° (d) 110°
  19. 19.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 25° (c) 65° (d) 130°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 140° (c) 100° (d) 280°
  21. 21.Two angles of a triangle are 30° and 115°. What is the exterior angle at the third corner? (a) 150° (b) 35° (c) 65° (d) 145°
  22. 22.Two angles of a triangle are 45° and 40°. What is the third angle? (a) 85° (b) 95° (c) 140° (d) 135°
  23. 23.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 60° (b) 160° (c) 120° (d) 140°
  24. 24.Two angles of a triangle are 50° and 55°. What is the third angle? (a) 75° (b) 130° (c) 125° (d) 105°
  25. 25.Two angles of a triangle are 45° and 35°. What is the exterior angle at the third corner? (a) 135° (b) 80° (c) 100° (d) 145°
  26. 26.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 70° (c) 130° (d) 110°
  27. 27.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 100° (c) 145° (d) 80°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 41° (b) 40° (c) 80° (d) 140°
  29. 29.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 50° (b) 51° (c) 130° (d) 230°
  30. 30.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 60° (c) 30° (d) 120°
  31. 31.Two angles of a triangle are 30° and 70°. What is the exterior angle at the third corner? (a) 80° (b) 150° (c) 100° (d) 110°
  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) 76° (b) 255° (c) 105° (d) 75°
  33. 33.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 140° (b) 135° (c) 95° (d) 85°
  34. 34.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 255° (c) 105° (d) 75°
  35. 35.Two angles of a triangle are 50° and 55°. What is the exterior angle at the third corner? (a) 75° (b) 130° (c) 125° (d) 105°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 250° (b) 70° (c) 55° (d) 125°
  37. 37.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 155° (d) 70°
  38. 38.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 85° (c) 10° (d) 5°
  39. 39.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) 335° (d) 25°
  40. 40.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 125° (b) 135° (c) 100° (d) 80°

Answer key

  1. 25°
  2. 45°
  3. 20°
  4. 125°
  5. 135°
  6. 80°
  7. 55°
  8. 105°
  9. 110°
  10. 150°
  11. 100°
  12. 100°
  13. 125°
  14. 40°
  15. 30°
  16. 15°
  17. 60°
  18. 80°
  19. 130°
  20. 140°
  21. 145°
  22. 95°
  23. 60°
  24. 75°
  25. 80°
  26. 70°
  27. 100°
  28. 40°
  29. 50°
  30. 60°
  31. 100°
  32. 75°
  33. 85°
  34. 105°
  35. 105°
  36. 125°
  37. 135°
  38. 10°
  39. 155°
  40. 80°

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