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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 48 · 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 80° and 50°. What is the third angle? (a) 230° (b) 100° (c) 50° (d) 130°
  2. 2.Two angles of a triangle are 30° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 70° (c) 110° (d) 150°
  3. 3.Two angles of a triangle are 30° and 75°. What is the third angle? (a) 255° (b) 105° (c) 150° (d) 75°
  4. 4.Two angles of a triangle are 45° and 30°. What is the third angle? (a) 105° (b) 135° (c) 75° (d) 150°
  5. 5.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 60° (c) 30° (d) 61°
  6. 6.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 145° (b) 100° (c) 115° (d) 35°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 100° (c) 50° (d) 40°
  8. 8.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 100° (b) 125° (c) 135° (d) 45°
  9. 9.Two angles of a triangle are 45° and 45°. What is the exterior angle at the third corner? (a) 270° (b) 135° (c) 91° (d) 90°
  10. 10.Two angles of a triangle are 50° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 35° (c) 130° (d) 145°
  11. 11.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 130° (b) 155° (c) 25° (d) 310°
  12. 12.Two angles of a triangle are 60° and 95°. What is the third angle? (a) 85° (b) 25° (c) 155° (d) 120°
  13. 13.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 45° (b) 100° (c) 135° (d) 125°
  14. 14.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 150° (c) 30° (d) 60°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 80° (c) 20° (d) 70°
  16. 16.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 100° (c) 40° (d) 50°
  17. 17.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 115° (c) 25° (d) 65°
  18. 18.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 200° (b) 160° (c) 20° (d) 21°
  19. 19.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) 130° (d) 25°
  20. 20.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 150° (b) 210° (c) 31° (d) 30°
  21. 21.Two angles of a triangle are 60° and 45°. What is the exterior angle at the third corner? (a) 120° (b) 135° (c) 75° (d) 105°
  22. 22.Two angles of a triangle are 50° and 80°. What is the exterior angle at the third corner? (a) 50° (b) 100° (c) 230° (d) 130°
  23. 23.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 75° (b) 285° (c) 15° (d) 105°
  24. 24.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 50° (c) 140° (d) 70°
  25. 25.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 50° (c) 80° (d) 40°
  26. 26.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 30° (c) 15° (d) 150°
  27. 27.Two angles of a triangle are 30° and 100°. What is the third angle? (a) 130° (b) 150° (c) 50° (d) 80°
  28. 28.Two angles of a triangle are 65° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 115° (c) 65° (d) 245°
  29. 29.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 105° (b) 75° (c) 145° (d) 110°
  30. 30.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 325° (b) 55° (c) 35° (d) 145°
  31. 31.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 115° (c) 45° (d) 135°
  32. 32.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 115° (b) 230° (c) 50° (d) 65°
  33. 33.Two angles of a triangle are 55° and 50°. What is the third angle? (a) 105° (b) 130° (c) 75° (d) 125°
  34. 34.Two angles of a triangle are 35° and 90°. What is the third angle? (a) 90° (b) 125° (c) 55° (d) 145°
  35. 35.Two angles of a triangle are 65° and 100°. What is the third angle? (a) 165° (b) 80° (c) 115° (d) 15°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 81° (b) 100° (c) 160° (d) 80°
  37. 37.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 125° (b) 115° (c) 120° (d) 60°
  38. 38.Two angles of a triangle are 25° and 95°. What is the exterior angle at the third corner? (a) 155° (b) 60° (c) 85° (d) 120°
  39. 39.Two angles of a triangle are 50° and 115°. What is the third angle? (a) 130° (b) 165° (c) 65° (d) 15°
  40. 40.Two angles of a triangle are 50° and 20°. What is the third angle? (a) 130° (b) 70° (c) 160° (d) 110°

Answer key

  1. 50°
  2. 70°
  3. 75°
  4. 105°
  5. 60°
  6. 145°
  7. 40°
  8. 45°
  9. 90°
  10. 145°
  11. 155°
  12. 25°
  13. 135°
  14. 120°
  15. 80°
  16. 100°
  17. 50°
  18. 20°
  19. 25°
  20. 30°
  21. 105°
  22. 130°
  23. 105°
  24. 70°
  25. 80°
  26. 15°
  27. 50°
  28. 115°
  29. 75°
  30. 145°
  31. 135°
  32. 115°
  33. 75°
  34. 55°
  35. 15°
  36. 80°
  37. 60°
  38. 120°
  39. 15°
  40. 110°

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