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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 240 · 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 165°. What is the angle next to it on the same straight line? (a) 195° (b) 15° (c) 165° (d) 16°
  2. 2.Two angles of a triangle are 20° and 70°. What is the exterior angle at the third corner? (a) 90° (b) 270° (c) 160° (d) 110°
  3. 3.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 140° (b) 145° (c) 75° (d) 105°
  4. 4.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 60° (c) 150° (d) 120°
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 100° (c) 280° (d) 140°
  6. 6.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 65° (c) 50° (d) 130°
  7. 7.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 100° (c) 80° (d) 105°
  8. 8.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 110° (c) 35° (d) 55°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 35° (c) 70° (d) 45°
  10. 10.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°
  11. 11.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 15° (b) 155° (c) 165° (d) 40°
  12. 12.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 30° (b) 150° (c) 105° (d) 210°
  13. 13.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 145° (b) 290° (c) 35° (d) 110°
  14. 14.Two angles of a triangle are 40° and 90°. What is the third angle? (a) 90° (b) 130° (c) 50° (d) 140°
  15. 15.Two angles of a triangle are 25° and 90°. What is the third angle? (a) 155° (b) 115° (c) 90° (d) 65°
  16. 16.Two angles of a triangle are 35° and 55°. What is the third angle? (a) 145° (b) 90° (c) 125° (d) 270°
  17. 17.Two angles of a triangle are 30° and 95°. What is the third angle? (a) 85° (b) 55° (c) 125° (d) 150°
  18. 18.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 160° (c) 70° (d) 80°
  19. 19.Two angles of a triangle are 25° and 60°. What is the third angle? (a) 120° (b) 155° (c) 95° (d) 85°
  20. 20.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 50° (c) 100° (d) 140°
  21. 21.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 150° (b) 270° (c) 120° (d) 90°
  22. 22.Two angles of a triangle are 75° and 70°. What is the exterior angle at the third corner? (a) 145° (b) 35° (c) 105° (d) 110°
  23. 23.Two angles of a triangle are 30° and 110°. What is the third angle? (a) 70° (b) 140° (c) 150° (d) 40°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 250° (b) 70° (c) 125° (d) 55°
  25. 25.Two angles of a triangle are 20° and 80°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 160° (d) 260°
  26. 26.Two angles of a triangle are 45° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 270° (c) 90° (d) 91°
  27. 27.Two angles of a triangle are 30° and 85°. What is the third angle? (a) 115° (b) 95° (c) 150° (d) 65°
  28. 28.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 60° (c) 150° (d) 30°
  29. 29.Two angles of a triangle are 25° and 45°. What is the third angle? (a) 135° (b) 155° (c) 110° (d) 70°
  30. 30.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 120° (b) 240° (c) 61° (d) 60°
  31. 31.Two angles of a triangle are 20° and 125°. What is the exterior angle at the third corner? (a) 145° (b) 35° (c) 160° (d) 55°
  32. 32.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 145° (b) 270° (c) 125° (d) 90°
  33. 33.Two angles of a triangle are 60° and 85°. What is the third angle? (a) 145° (b) 95° (c) 120° (d) 35°
  34. 34.Two angles of a triangle are 75° and 40°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 140° (d) 105°
  35. 35.Two angles of a triangle are 35° and 100°. What is the third angle? (a) 80° (b) 45° (c) 145° (d) 135°
  36. 36.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 100° (b) 120° (c) 60° (d) 140°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 66° (b) 65° (c) 115° (d) 130°
  38. 38.Two angles of a triangle are 70° and 65°. What is the exterior angle at the third corner? (a) 110° (b) 115° (c) 135° (d) 45°
  39. 39.Two angles of a triangle are 60° and 110°. What is the third angle? (a) 120° (b) 10° (c) 170° (d) 70°
  40. 40.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°

Answer key

  1. 15°
  2. 90°
  3. 105°
  4. 120°
  5. 140°
  6. 65°
  7. 100°
  8. 110°
  9. 35°
  10. 45°
  11. 15°
  12. 30°
  13. 145°
  14. 50°
  15. 65°
  16. 90°
  17. 55°
  18. 80°
  19. 95°
  20. 100°
  21. 90°
  22. 145°
  23. 40°
  24. 125°
  25. 100°
  26. 90°
  27. 65°
  28. 75°
  29. 110°
  30. 60°
  31. 145°
  32. 90°
  33. 35°
  34. 115°
  35. 45°
  36. 60°
  37. 65°
  38. 135°
  39. 10°
  40. 70°

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