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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 68 · 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 straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 170° (b) 10° (c) 190° (d) 11°
  2. 2.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 145° (b) 100° (c) 65° (d) 115°
  3. 3.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) 110° (c) 70° (d) 20°
  4. 4.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 85° (c) 265° (d) 95°
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 26° (b) 155° (c) 25° (d) 50°
  6. 6.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 50° (b) 130° (c) 310° (d) 40°
  7. 7.Two angles of a triangle are 25° and 25°. What is the third angle? (a) 310° (b) 155° (c) 130° (d) 50°
  8. 8.Two angles of a triangle are 40° and 100°. What is the third angle? (a) 40° (b) 140° (c) 80° (d) 220°
  9. 9.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 135° (c) 150° (d) 30°
  10. 10.Two angles of a triangle are 25° and 125°. What is the exterior angle at the third corner? (a) 30° (b) 55° (c) 150° (d) 155°
  11. 11.Two angles of a triangle are 30° and 100°. What is the third angle? (a) 50° (b) 150° (c) 130° (d) 80°
  12. 12.Two angles of a triangle are 80° and 60°. What is the third angle? (a) 120° (b) 140° (c) 100° (d) 40°
  13. 13.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 40° (c) 100° (d) 80°
  14. 14.Two angles of a triangle are 20° and 45°. What is the exterior angle at the third corner? (a) 160° (b) 65° (c) 135° (d) 115°
  15. 15.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 95° (b) 145° (c) 130° (d) 85°
  16. 16.Two angles of a triangle are 50° and 105°. What is the third angle? (a) 25° (b) 155° (c) 75° (d) 130°
  17. 17.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) 15° (c) 105° (d) 75°
  18. 18.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 110° (b) 140° (c) 71° (d) 70°
  19. 19.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 30° (c) 15° (d) 75°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 110° (b) 70° (c) 40° (d) 220°
  21. 21.Two angles of a triangle are 35° and 105°. What is the third angle? (a) 140° (b) 75° (c) 145° (d) 40°
  22. 22.Two angles of a triangle are 25° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 130° (c) 50° (d) 310°
  23. 23.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 125° (b) 135° (c) 100° (d) 45°
  24. 24.Two angles of a triangle are 25° and 90°. What is the third angle? (a) 65° (b) 90° (c) 115° (d) 155°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 50° (c) 35° (d) 25°
  26. 26.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 335° (b) 25° (c) 155° (d) 65°
  27. 27.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 75° (c) 30° (d) 60°
  28. 28.Two angles of a triangle are 35° and 90°. What is the third angle? (a) 145° (b) 90° (c) 125° (d) 55°
  29. 29.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 45° (c) 70° (d) 110°
  30. 30.Two angles of a triangle are 45° and 30°. What is the third angle? (a) 105° (b) 75° (c) 150° (d) 135°
  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 25° and 140°. What is the third angle? (a) 155° (b) 40° (c) 165° (d) 15°
  33. 33.Two angles of a triangle are 50° and 115°. What is the third angle? (a) 15° (b) 165° (c) 130° (d) 65°
  34. 34.Two angles of a triangle are 75° and 30°. What is the third angle? (a) 255° (b) 75° (c) 150° (d) 105°
  35. 35.Two angles of a triangle are 40° and 75°. What is the third angle? (a) 115° (b) 105° (c) 65° (d) 140°
  36. 36.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 70° (b) 250° (c) 110° (d) 71°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 120° (c) 60° (d) 70°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 130° (b) 66° (c) 65° (d) 115°
  39. 39.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) 75° (d) 105°
  40. 40.Two angles of a triangle are 45° and 90°. What is the third angle? (a) 225° (b) 90° (c) 45° (d) 135°

Answer key

  1. 10°
  2. 65°
  3. 110°
  4. 85°
  5. 25°
  6. 130°
  7. 130°
  8. 40°
  9. 150°
  10. 150°
  11. 50°
  12. 40°
  13. 40°
  14. 65°
  15. 85°
  16. 25°
  17. 105°
  18. 70°
  19. 30°
  20. 110°
  21. 40°
  22. 50°
  23. 45°
  24. 65°
  25. 25°
  26. 155°
  27. 75°
  28. 55°
  29. 35°
  30. 105°
  31. 40°
  32. 15°
  33. 15°
  34. 75°
  35. 65°
  36. 70°
  37. 60°
  38. 65°
  39. 75°
  40. 45°

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