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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 139 · 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 45° and 65°. What is the exterior angle at the third corner? (a) 135° (b) 115° (c) 70° (d) 110°
  2. 2.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 95° (b) 130° (c) 45° (d) 135°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 60° (c) 75° (d) 150°
  4. 4.Two angles of a triangle are 65° and 100°. What is the third angle? (a) 165° (b) 115° (c) 80° (d) 15°
  5. 5.Two angles of a triangle are 50° and 45°. What is the third angle? (a) 95° (b) 85° (c) 135° (d) 130°
  6. 6.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 120° (b) 75° (c) 135° (d) 105°
  7. 7.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 300° (b) 30° (c) 120° (d) 60°
  8. 8.Two angles of a triangle are 30° and 45°. What is the third angle? (a) 75° (b) 135° (c) 105° (d) 150°
  9. 9.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°
  10. 10.Two angles of a triangle are 60° and 60°. What is the third angle? (a) 120° (b) 61° (c) 240° (d) 60°
  11. 11.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 45° (b) 135° (c) 90° (d) 270°
  12. 12.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) 40° (d) 50°
  13. 13.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 70° (c) 80° (d) 20°
  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) 40° (c) 50° (d) 80°
  15. 15.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 100° (b) 75° (c) 155° (d) 105°
  16. 16.Two angles of a triangle are 60° and 35°. What is the third angle? (a) 95° (b) 120° (c) 85° (d) 145°
  17. 17.Two angles of a triangle are 60° and 55°. What is the third angle? (a) 65° (b) 125° (c) 115° (d) 120°
  18. 18.Two angles of a triangle are 60° and 25°. What is the exterior angle at the third corner? (a) 85° (b) 120° (c) 155° (d) 95°
  19. 19.Two angles of a triangle are 45° and 70°. What is the third angle? (a) 135° (b) 65° (c) 115° (d) 110°
  20. 20.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 130° (c) 155° (d) 75°
  21. 21.Two angles of a triangle are 45° and 105°. What is the third angle? (a) 30° (b) 135° (c) 75° (d) 150°
  22. 22.Two angles of a triangle are 55° and 25°. What is the third angle? (a) 155° (b) 125° (c) 80° (d) 100°
  23. 23.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 130° (b) 40° (c) 310° (d) 50°
  24. 24.Two angles of a triangle are 25° and 105°. What is the third angle? (a) 130° (b) 155° (c) 75° (d) 50°
  25. 25.Two angles of a triangle are 50° and 50°. What is the exterior angle at the third corner? (a) 260° (b) 130° (c) 100° (d) 80°
  26. 26.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 10° (b) 100° (c) 80° (d) 280°
  27. 27.Two angles of a triangle are 45° and 50°. What is the third angle? (a) 95° (b) 135° (c) 130° (d) 85°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 130° (b) 51° (c) 100° (d) 50°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 10° (b) 95° (c) 190° (d) 85°
  30. 30.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 50° (c) 25° (d) 130°
  31. 31.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 70° (c) 40° (d) 110°
  32. 32.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 70° (c) 110° (d) 160°
  33. 33.Two angles of a triangle are 45° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 75° (c) 105° (d) 135°
  34. 34.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 155° (b) 125° (c) 80° (d) 25°
  35. 35.Two angles of a triangle are 35° and 95°. What is the third angle? (a) 85° (b) 50° (c) 145° (d) 130°
  36. 36.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 80° (c) 40° (d) 50°
  37. 37.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) 105° (c) 76° (d) 75°
  38. 38.Two angles of a triangle are 25° and 125°. What is the exterior angle at the third corner? (a) 155° (b) 150° (c) 30° (d) 55°
  39. 39.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 150° (b) 160° (c) 20° (d) 50°
  40. 40.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 70° (b) 290° (c) 20° (d) 110°

Answer key

  1. 110°
  2. 45°
  3. 75°
  4. 15°
  5. 85°
  6. 75°
  7. 120°
  8. 105°
  9. 15°
  10. 60°
  11. 135°
  12. 140°
  13. 80°
  14. 40°
  15. 105°
  16. 85°
  17. 65°
  18. 85°
  19. 65°
  20. 75°
  21. 30°
  22. 100°
  23. 130°
  24. 50°
  25. 100°
  26. 100°
  27. 85°
  28. 50°
  29. 95°
  30. 25°
  31. 40°
  32. 70°
  33. 105°
  34. 25°
  35. 50°
  36. 80°
  37. 75°
  38. 150°
  39. 20°
  40. 110°

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