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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 445 · 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 25°. What is the angle next to it on the same straight line? (a) 65° (b) 335° (c) 155° (d) 25°
  2. 2.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 60° (b) 120° (c) 300° (d) 30°
  3. 3.Two angles of a triangle are 25° and 70°. What is the third angle? (a) 95° (b) 110° (c) 85° (d) 155°
  4. 4.Two angles of a triangle are 70° and 75°. What is the third angle? (a) 145° (b) 110° (c) 35° (d) 105°
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 165° (b) 16° (c) 15° (d) 30°
  6. 6.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 25° (b) 155° (c) 80° (d) 125°
  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 40° and 60°. What is the third angle? (a) 120° (b) 80° (c) 100° (d) 140°
  9. 9.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 91° (c) 135° (d) 90°
  10. 10.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 45° (c) 110° (d) 35°
  11. 11.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) 25° (d) 130°
  12. 12.Two angles of a triangle are 25° and 120°. What is the third angle? (a) 155° (b) 60° (c) 145° (d) 35°
  13. 13.Two angles of a triangle are 25° and 65°. What is the third angle? (a) 155° (b) 270° (c) 90° (d) 115°
  14. 14.Two angles of a triangle are 50° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 145° (c) 130° (d) 35°
  15. 15.Two angles of a triangle are 75° and 75°. What is the exterior angle at the third corner? (a) 150° (b) 210° (c) 105° (d) 30°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 155° (b) 25° (c) 50° (d) 26°
  17. 17.Two angles of a triangle are 30° and 55°. What is the exterior angle at the third corner? (a) 85° (b) 125° (c) 95° (d) 150°
  18. 18.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 45° (b) 135° (c) 270° (d) 90°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 40° (c) 50° (d) 70°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 190° (b) 85° (c) 95° (d) 10°
  21. 21.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 30° (c) 60° (d) 75°
  22. 22.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 70° (b) 110° (c) 120° (d) 130°
  23. 23.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 105° (b) 170° (c) 85° (d) 10°
  24. 24.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) 70° (d) 20°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 70° (c) 55° (d) 20°
  26. 26.Two angles of a triangle are 45° and 85°. What is the third angle? (a) 95° (b) 50° (c) 135° (d) 130°
  27. 27.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 50° (c) 10° (d) 100°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 100° (b) 81° (c) 160° (d) 80°
  29. 29.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) 40° (d) 310°
  30. 30.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 115° (c) 50° (d) 25°
  31. 31.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) 75° (c) 255° (d) 76°
  32. 32.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) 250° (c) 110° (d) 70°
  33. 33.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 165° (b) 15° (c) 40° (d) 155°
  34. 34.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 95° (c) 85° (d) 86°
  35. 35.Two angles of a triangle are 35° and 55°. What is the third angle? (a) 270° (b) 125° (c) 90° (d) 145°
  36. 36.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 46° (c) 55° (d) 90°
  37. 37.Two angles of a triangle are 35° and 75°. What is the third angle? (a) 105° (b) 110° (c) 70° (d) 145°
  38. 38.Two angles of a triangle are 20° and 90°. What is the third angle? (a) 90° (b) 160° (c) 70° (d) 110°
  39. 39.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 120° (b) 60° (c) 155° (d) 145°
  40. 40.Two angles of a triangle are 60° and 60°. What is the third angle? (a) 61° (b) 60° (c) 240° (d) 120°

Answer key

  1. 155°
  2. 120°
  3. 85°
  4. 35°
  5. 15°
  6. 25°
  7. 40°
  8. 80°
  9. 90°
  10. 35°
  11. 25°
  12. 35°
  13. 90°
  14. 145°
  15. 150°
  16. 25°
  17. 85°
  18. 135°
  19. 70°
  20. 95°
  21. 75°
  22. 70°
  23. 10°
  24. 80°
  25. 55°
  26. 50°
  27. 50°
  28. 80°
  29. 130°
  30. 50°
  31. 75°
  32. 70°
  33. 15°
  34. 85°
  35. 90°
  36. 45°
  37. 70°
  38. 70°
  39. 60°
  40. 60°

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