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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 395 · 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.

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  1. 1.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 60° (b) 240° (c) 120° (d) 61°
  2. 2.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) 31° (c) 30° (d) 210°
  3. 3.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 80° (b) 150° (c) 100° (d) 130°
  4. 4.Two angles of a triangle are 55° and 50°. What is the third angle? (a) 75° (b) 130° (c) 105° (d) 125°
  5. 5.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 95° (b) 130° (c) 85° (d) 145°
  6. 6.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) 150° (d) 75°
  7. 7.Two angles of a triangle are 75° and 85°. What is the third angle? (a) 105° (b) 20° (c) 160° (d) 95°
  8. 8.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 20° (c) 10° (d) 100°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 25° (c) 35° (d) 130°
  10. 10.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 85° (b) 105° (c) 160° (d) 95°
  11. 11.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) 155° (c) 65° (d) 25°
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 210° (b) 75° (c) 105° (d) 30°
  13. 13.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 20° (c) 110° (d) 40°
  14. 14.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 100° (b) 81° (c) 260° (d) 80°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 40° (c) 130° (d) 65°
  16. 16.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 150° (b) 30° (c) 60° (d) 330°
  17. 17.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 255° (c) 75° (d) 105°
  18. 18.Two angles of a triangle are 45° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 135° (c) 95° (d) 85°
  19. 19.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 120° (b) 115° (c) 125° (d) 60°
  20. 20.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 35° (c) 70° (d) 55°
  21. 21.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 135° (b) 45° (c) 270° (d) 90°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 110° (b) 220° (c) 70° (d) 40°
  23. 23.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 165° (b) 155° (c) 15° (d) 40°
  24. 24.Two angles of a triangle are 60° and 50°. What is the third angle? (a) 110° (b) 70° (c) 130° (d) 120°
  25. 25.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 105° (b) 255° (c) 75° (d) 76°
  26. 26.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 145° (b) 36° (c) 215° (d) 35°
  27. 27.Two angles of a triangle are 45° and 115°. What is the third angle? (a) 135° (b) 160° (c) 65° (d) 20°
  28. 28.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 205° (b) 25° (c) 26° (d) 155°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 70° (b) 36° (c) 145° (d) 35°
  30. 30.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 10° (b) 170° (c) 190° (d) 11°
  31. 31.Two angles of a triangle are 30° and 75°. What is the exterior angle at the third corner? (a) 75° (b) 150° (c) 105° (d) 255°
  32. 32.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 125° (b) 70° (c) 55° (d) 250°
  33. 33.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 235° (b) 55° (c) 56° (d) 125°
  34. 34.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 71° (b) 70° (c) 110° (d) 250°
  35. 35.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 80° (b) 100° (c) 280° (d) 10°
  36. 36.Two angles of a triangle are 60° and 70°. What is the third angle? (a) 120° (b) 110° (c) 130° (d) 50°
  37. 37.Two angles of a triangle are 40° and 30°. What is the exterior angle at the third corner? (a) 110° (b) 140° (c) 70° (d) 150°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 60° (c) 70° (d) 30°
  39. 39.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 80° (c) 10° (d) 100°
  40. 40.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 50° (c) 130° (d) 80°

Answer key

  1. 60°
  2. 30°
  3. 100°
  4. 75°
  5. 95°
  6. 75°
  7. 20°
  8. 20°
  9. 25°
  10. 95°
  11. 155°
  12. 105°
  13. 40°
  14. 80°
  15. 65°
  16. 150°
  17. 105°
  18. 85°
  19. 60°
  20. 70°
  21. 135°
  22. 110°
  23. 15°
  24. 70°
  25. 75°
  26. 35°
  27. 20°
  28. 25°
  29. 35°
  30. 10°
  31. 105°
  32. 125°
  33. 55°
  34. 70°
  35. 100°
  36. 50°
  37. 70°
  38. 60°
  39. 50°
  40. 80°

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