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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 420 · 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 80°. What is the angle next to it on the same straight line? (a) 10° (b) 80° (c) 280° (d) 100°
  2. 2.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 125° (c) 55° (d) 70°
  3. 3.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 265° (c) 86° (d) 95°
  4. 4.Two angles of a triangle are 60° and 80°. What is the third angle? (a) 40° (b) 120° (c) 100° (d) 140°
  5. 5.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°
  6. 6.Two angles of a triangle are 25° and 25°. What is the exterior angle at the third corner? (a) 310° (b) 50° (c) 155° (d) 130°
  7. 7.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) 11° (c) 190° (d) 170°
  8. 8.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 115° (b) 105° (c) 140° (d) 65°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 30° (b) 120° (c) 300° (d) 150°
  10. 10.Two angles of a triangle are 75° and 40°. What is the exterior angle at the third corner? (a) 105° (b) 115° (c) 140° (d) 65°
  11. 11.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 120° (b) 60° (c) 40° (d) 30°
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 70° (b) 35° (c) 145° (d) 36°
  13. 13.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 130° (b) 75° (c) 105° (d) 155°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 80° (b) 100° (c) 20° (d) 200°
  15. 15.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 110° (c) 80° (d) 100°
  16. 16.Two angles of a triangle are 45° and 110°. What is the third angle? (a) 70° (b) 135° (c) 155° (d) 25°
  17. 17.Two angles of a triangle are 50° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 260° (c) 100° (d) 80°
  18. 18.Two angles of a triangle are 35° and 30°. What is the third angle? (a) 145° (b) 65° (c) 150° (d) 115°
  19. 19.Two angles of a triangle are 45° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 135° (c) 115° (d) 65°
  20. 20.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 150° (b) 80° (c) 100° (d) 110°
  21. 21.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) 150° (d) 15°
  22. 22.Two angles of a triangle are 65° and 65°. What is the third angle? (a) 130° (b) 115° (c) 230° (d) 50°
  23. 23.Two angles of a triangle are 60° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 95° (c) 120° (d) 85°
  24. 24.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 70° (c) 40° (d) 140°
  25. 25.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 45° (b) 100° (c) 125° (d) 135°
  26. 26.Two angles of a triangle are 40° and 40°. What is the exterior angle at the third corner? (a) 280° (b) 100° (c) 80° (d) 140°
  27. 27.Two angles of a triangle are 45° and 65°. What is the exterior angle at the third corner? (a) 110° (b) 135° (c) 115° (d) 70°
  28. 28.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 60° (c) 120° (d) 61°
  29. 29.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 150° (b) 100° (c) 130° (d) 80°
  30. 30.Two angles of a triangle are 25° and 85°. What is the third angle? (a) 95° (b) 110° (c) 70° (d) 155°
  31. 31.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 100° (c) 40° (d) 140°
  32. 32.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 85° (b) 160° (c) 95° (d) 105°
  33. 33.Two angles of a triangle are 60° and 60°. What is the third angle? (a) 60° (b) 120° (c) 240° (d) 61°
  34. 34.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 40° (c) 130° (d) 50°
  35. 35.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 15° (b) 16° (c) 195° (d) 165°
  36. 36.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 30° (c) 150° (d) 120°
  37. 37.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 80° (c) 10° (d) 20°
  38. 38.Two angles of a triangle are 70° and 100°. What is the third angle? (a) 80° (b) 10° (c) 110° (d) 170°
  39. 39.Two angles of a triangle are 75° and 45°. What is the third angle? (a) 105° (b) 60° (c) 135° (d) 120°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 81° (b) 80° (c) 100° (d) 160°

Answer key

  1. 100°
  2. 70°
  3. 85°
  4. 40°
  5. 75°
  6. 50°
  7. 10°
  8. 65°
  9. 150°
  10. 115°
  11. 30°
  12. 35°
  13. 75°
  14. 100°
  15. 100°
  16. 25°
  17. 100°
  18. 115°
  19. 115°
  20. 80°
  21. 15°
  22. 50°
  23. 85°
  24. 70°
  25. 135°
  26. 80°
  27. 110°
  28. 60°
  29. 100°
  30. 70°
  31. 140°
  32. 95°
  33. 60°
  34. 80°
  35. 15°
  36. 120°
  37. 20°
  38. 10°
  39. 60°
  40. 80°

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