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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 757 · 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 75° each. What is the third angle? (a) 15° (b) 30° (c) 75° (d) 105°
  2. 2.Two angles of a triangle are 40° and 100°. What is the exterior angle at the third corner? (a) 40° (b) 80° (c) 220° (d) 140°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 140° (c) 70° (d) 40°
  4. 4.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 160° (b) 150° (c) 50° (d) 20°
  5. 5.Two angles of a triangle are 30° and 95°. What is the exterior angle at the third corner? (a) 150° (b) 85° (c) 55° (d) 125°
  6. 6.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 41° (b) 140° (c) 40° (d) 220°
  7. 7.Two angles of a triangle are 40° and 125°. What is the third angle? (a) 15° (b) 55° (c) 140° (d) 165°
  8. 8.Two angles of a triangle are 80° and 70°. What is the third angle? (a) 100° (b) 150° (c) 110° (d) 30°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 140° (b) 80° (c) 40° (d) 41°
  10. 10.Two angles of a triangle are 50° and 50°. What is the third angle? (a) 130° (b) 80° (c) 100° (d) 260°
  11. 11.Two angles of a triangle are 60° and 85°. What is the third angle? (a) 145° (b) 120° (c) 35° (d) 95°
  12. 12.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 145° (c) 110° (d) 35°
  13. 13.Two angles of a triangle are 50° and 70°. What is the third angle? (a) 110° (b) 120° (c) 60° (d) 130°
  14. 14.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 160° (b) 85° (c) 105° (d) 95°
  15. 15.Two angles of a triangle are 35° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 145° (c) 140° (d) 40°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 135° (b) 45° (c) 46° (d) 90°
  17. 17.Two angles of a triangle are 25° and 75°. What is the exterior angle at the third corner? (a) 80° (b) 105° (c) 100° (d) 155°
  18. 18.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 135° (b) 225° (c) 46° (d) 45°
  19. 19.Two angles of a triangle are 40° and 70°. What is the third angle? (a) 70° (b) 140° (c) 250° (d) 110°
  20. 20.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 70° (c) 20° (d) 110°
  21. 21.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 170° (c) 95° (d) 86°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 210° (b) 105° (c) 75° (d) 30°
  23. 23.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 150° (b) 35° (c) 145° (d) 65°
  24. 24.Two angles of a triangle are 20° and 140°. What is the third angle? (a) 160° (b) 200° (c) 20° (d) 40°
  25. 25.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 91° (c) 135° (d) 90°
  26. 26.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 110° (b) 70° (c) 250° (d) 140°
  27. 27.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 90° (b) 145° (c) 270° (d) 125°
  28. 28.Two angles of a triangle are 50° and 95°. What is the third angle? (a) 145° (b) 85° (c) 35° (d) 130°
  29. 29.Two angles of a triangle are 45° and 60°. What is the exterior angle at the third corner? (a) 135° (b) 120° (c) 75° (d) 105°
  30. 30.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 120° (b) 30° (c) 60° (d) 300°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 70° (c) 110° (d) 45°
  32. 32.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 290° (b) 20° (c) 70° (d) 110°
  33. 33.Two angles of a triangle are 55° and 55°. What is the third angle? (a) 70° (b) 125° (c) 250° (d) 110°
  34. 34.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 75° (b) 105° (c) 135° (d) 120°
  35. 35.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 110° (b) 135° (c) 115° (d) 70°
  36. 36.Two angles of a triangle are 30° and 95°. What is the third angle? (a) 150° (b) 125° (c) 55° (d) 85°
  37. 37.Two angles of a triangle are 25° and 50°. What is the third angle? (a) 130° (b) 155° (c) 75° (d) 105°
  38. 38.Two angles of a triangle are 75° and 30°. What is the third angle? (a) 150° (b) 105° (c) 75° (d) 255°
  39. 39.Two angles of a triangle are 30° and 80°. What is the exterior angle at the third corner? (a) 70° (b) 100° (c) 110° (d) 150°
  40. 40.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 25° (b) 50° (c) 130° (d) 35°

Answer key

  1. 30°
  2. 140°
  3. 70°
  4. 20°
  5. 125°
  6. 40°
  7. 15°
  8. 30°
  9. 40°
  10. 80°
  11. 35°
  12. 110°
  13. 60°
  14. 85°
  15. 140°
  16. 45°
  17. 100°
  18. 45°
  19. 70°
  20. 40°
  21. 85°
  22. 105°
  23. 35°
  24. 20°
  25. 90°
  26. 70°
  27. 90°
  28. 35°
  29. 105°
  30. 120°
  31. 35°
  32. 110°
  33. 70°
  34. 75°
  35. 70°
  36. 55°
  37. 105°
  38. 75°
  39. 110°
  40. 25°

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