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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 111 · 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 angles of a triangle are 35° and 90°. What is the third angle? (a) 125° (b) 90° (c) 145° (d) 55°
  2. 2.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 110° (c) 40° (d) 70°
  3. 3.Two angles of a triangle are 45° and 60°. What is the third angle? (a) 120° (b) 135° (c) 105° (d) 75°
  4. 4.Two angles of a triangle are 40° and 75°. What is the exterior angle at the third corner? (a) 115° (b) 65° (c) 105° (d) 140°
  5. 5.Two angles of a triangle are 40° and 60°. What is the third angle? (a) 80° (b) 120° (c) 140° (d) 100°
  6. 6.Two angles of a triangle are 45° and 85°. What is the third angle? (a) 50° (b) 135° (c) 130° (d) 95°
  7. 7.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) 265° (c) 95° (d) 85°
  8. 8.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) 90° (d) 55°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 30° (c) 15° (d) 25°
  10. 10.Two angles of a triangle are 35° and 110°. What is the exterior angle at the third corner? (a) 35° (b) 215° (c) 145° (d) 70°
  11. 11.Two angles of a triangle are 65° and 100°. What is the third angle? (a) 115° (b) 15° (c) 80° (d) 165°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 40° (c) 50° (d) 140°
  13. 13.Two angles of a triangle are 20° and 95°. What is the third angle? (a) 85° (b) 115° (c) 160° (d) 65°
  14. 14.Two angles of a triangle are 35° and 80°. What is the third angle? (a) 65° (b) 115° (c) 100° (d) 145°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 80° (b) 20° (c) 100° (d) 200°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 165° (b) 30° (c) 16° (d) 15°
  17. 17.Two angles of a triangle are 50° and 35°. What is the third angle? (a) 145° (b) 130° (c) 95° (d) 85°
  18. 18.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 235° (b) 55° (c) 125° (d) 110°
  19. 19.Two angles of a triangle are 30° and 50°. What is the third angle? (a) 80° (b) 150° (c) 100° (d) 130°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 25° (b) 26° (c) 50° (d) 155°
  21. 21.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 75° (c) 150° (d) 30°
  22. 22.Two angles of a triangle are 45° and 40°. What is the third angle? (a) 85° (b) 95° (c) 140° (d) 135°
  23. 23.Two angles of a triangle are 55° and 50°. What is the third angle? (a) 105° (b) 75° (c) 130° (d) 125°
  24. 24.Two angles of a triangle are 20° and 135°. What is the third angle? (a) 155° (b) 160° (c) 45° (d) 25°
  25. 25.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 210° (b) 30° (c) 150° (d) 31°
  26. 26.Two angles of a triangle are 75° and 80°. What is the third angle? (a) 105° (b) 100° (c) 25° (d) 155°
  27. 27.Two angles of a triangle are 25° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 55° (c) 125° (d) 155°
  28. 28.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 20° (c) 70° (d) 80°
  29. 29.Two angles of a triangle are 55° and 95°. What is the exterior angle at the third corner? (a) 150° (b) 30° (c) 125° (d) 85°
  30. 30.Two angles of a triangle are 35° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 80° (c) 145° (d) 100°
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 135° (b) 90° (c) 46° (d) 45°
  32. 32.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 51° (b) 50° (c) 230° (d) 130°
  33. 33.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 30° (b) 60° (c) 120° (d) 300°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 70° (b) 55° (c) 250° (d) 125°
  35. 35.Two angles of a triangle are 20° and 150°. What is the third angle? (a) 170° (b) 160° (c) 30° (d) 10°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 35° (b) 110° (c) 145° (d) 290°
  37. 37.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 200° (b) 20° (c) 160° (d) 21°
  38. 38.Two angles of a triangle are 75° and 40°. What is the exterior angle at the third corner? (a) 105° (b) 140° (c) 65° (d) 115°
  39. 39.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) 155° (c) 25° (d) 26°
  40. 40.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 95° (c) 10° (d) 85°

Answer key

  1. 55°
  2. 40°
  3. 75°
  4. 115°
  5. 80°
  6. 50°
  7. 85°
  8. 45°
  9. 15°
  10. 145°
  11. 15°
  12. 70°
  13. 65°
  14. 65°
  15. 100°
  16. 15°
  17. 95°
  18. 55°
  19. 100°
  20. 25°
  21. 75°
  22. 95°
  23. 75°
  24. 25°
  25. 30°
  26. 25°
  27. 125°
  28. 80°
  29. 150°
  30. 80°
  31. 45°
  32. 50°
  33. 120°
  34. 125°
  35. 10°
  36. 145°
  37. 20°
  38. 115°
  39. 25°
  40. 10°

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