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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 100 · 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 145°. What is the angle next to it on the same straight line? (a) 145° (b) 36° (c) 215° (d) 35°
  2. 2.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 170° (c) 86° (d) 95°
  3. 3.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 20° (b) 160° (c) 21° (d) 200°
  4. 4.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 55° (c) 35° (d) 110°
  5. 5.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 145° (b) 75° (c) 105° (d) 140°
  6. 6.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 140° (c) 40° (d) 70°
  7. 7.Two angles of a triangle are 30° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 110° (c) 150° (d) 70°
  8. 8.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 130° (c) 35° (d) 25°
  9. 9.Two angles of a triangle are 50° and 25°. What is the third angle? (a) 130° (b) 75° (c) 155° (d) 105°
  10. 10.Two angles of a triangle are 60° and 110°. What is the third angle? (a) 170° (b) 120° (c) 10° (d) 70°
  11. 11.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 145° (b) 155° (c) 120° (d) 60°
  12. 12.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 100° (c) 65° (d) 145°
  13. 13.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 41° (b) 220° (c) 140° (d) 40°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 90° (b) 135° (c) 270° (d) 45°
  15. 15.Two angles of a triangle are 55° and 70°. What is the exterior angle at the third corner? (a) 55° (b) 110° (c) 235° (d) 125°
  16. 16.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°
  17. 17.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 80° (b) 100° (c) 81° (d) 260°
  18. 18.Two angles of a triangle are 50° and 95°. What is the exterior angle at the third corner? (a) 130° (b) 145° (c) 35° (d) 85°
  19. 19.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 40° (b) 140° (c) 100° (d) 120°
  20. 20.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 135° (c) 91° (d) 45°
  21. 21.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 140° (d) 120°
  22. 22.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 45° (b) 100° (c) 125° (d) 135°
  23. 23.Two angles of a triangle are 60° and 50°. What is the third angle? (a) 110° (b) 120° (c) 130° (d) 70°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 46° (b) 90° (c) 135° (d) 45°
  25. 25.Two angles of a triangle are 60° and 60°. What is the third angle? (a) 240° (b) 120° (c) 61° (d) 60°
  26. 26.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 25° (b) 26° (c) 155° (d) 205°
  27. 27.Two angles of a triangle are 30° and 140°. What is the third angle? (a) 170° (b) 150° (c) 40° (d) 10°
  28. 28.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 50° (b) 40° (c) 140° (d) 320°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 65° (b) 130° (c) 66° (d) 115°
  30. 30.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 110° (c) 70° (d) 35°
  31. 31.Two angles of a triangle are 65° and 30°. What is the exterior angle at the third corner? (a) 85° (b) 150° (c) 115° (d) 95°
  32. 32.Two angles of a triangle are 30° and 80°. What is the third angle? (a) 150° (b) 110° (c) 100° (d) 70°
  33. 33.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 25° (b) 65° (c) 335° (d) 155°
  34. 34.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 140° (b) 70° (c) 250° (d) 110°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 190° (b) 10° (c) 95° (d) 85°
  36. 36.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) 16° (d) 165°
  37. 37.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 110° (b) 145° (c) 75° (d) 105°
  38. 38.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 120° (c) 60° (d) 30°
  39. 39.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 140° (b) 95° (c) 135° (d) 85°
  40. 40.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 130° (b) 120° (c) 70° (d) 110°

Answer key

  1. 35°
  2. 85°
  3. 20°
  4. 110°
  5. 105°
  6. 70°
  7. 110°
  8. 25°
  9. 105°
  10. 10°
  11. 120°
  12. 115°
  13. 40°
  14. 135°
  15. 125°
  16. 60°
  17. 80°
  18. 145°
  19. 140°
  20. 90°
  21. 100°
  22. 45°
  23. 70°
  24. 45°
  25. 60°
  26. 25°
  27. 10°
  28. 140°
  29. 65°
  30. 35°
  31. 95°
  32. 70°
  33. 155°
  34. 70°
  35. 95°
  36. 15°
  37. 75°
  38. 60°
  39. 85°
  40. 110°

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