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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 467 · 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.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 15° (c) 30° (d) 75°
  2. 2.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) 195° (c) 16° (d) 165°
  3. 3.Two angles of a triangle are 50° and 55°. What is the third angle? (a) 130° (b) 105° (c) 75° (d) 125°
  4. 4.Two angles of a triangle are 65° and 105°. What is the third angle? (a) 115° (b) 75° (c) 170° (d) 10°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 30° (c) 120° (d) 60°
  6. 6.Two angles of a triangle are 65° and 25°. What is the third angle? (a) 90° (b) 115° (c) 270° (d) 155°
  7. 7.Two angles of a triangle are 30° and 95°. What is the exterior angle at the third corner? (a) 150° (b) 125° (c) 85° (d) 55°
  8. 8.Two angles of a triangle are 35° and 25°. What is the third angle? (a) 120° (b) 145° (c) 60° (d) 155°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 105° (b) 210° (c) 75° (d) 30°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 110° (b) 125° (c) 56° (d) 55°
  11. 11.Two angles of a triangle are 20° and 135°. What is the third angle? (a) 160° (b) 45° (c) 25° (d) 155°
  12. 12.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) 205° (c) 26° (d) 155°
  13. 13.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 110° (c) 40° (d) 70°
  14. 14.Two angles of a triangle are 40° and 120°. What is the third angle? (a) 20° (b) 60° (c) 140° (d) 160°
  15. 15.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 130° (c) 80° (d) 100°
  16. 16.Two angles of a triangle are 40° and 85°. What is the exterior angle at the third corner? (a) 140° (b) 125° (c) 55° (d) 95°
  17. 17.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 150° (c) 15° (d) 25°
  18. 18.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 121° (b) 60° (c) 120° (d) 240°
  19. 19.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 250° (c) 110° (d) 70°
  20. 20.Two angles of a triangle are 20° and 45°. What is the third angle? (a) 135° (b) 160° (c) 115° (d) 65°
  21. 21.Two angles of a triangle are 45° and 125°. What is the third angle? (a) 55° (b) 135° (c) 170° (d) 10°
  22. 22.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 75° (b) 105° (c) 140° (d) 145°
  23. 23.Two angles of a triangle are 30° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 255° (c) 150° (d) 75°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 150° (b) 31° (c) 60° (d) 30°
  25. 25.Two angles of a triangle are 25° and 105°. What is the third angle? (a) 130° (b) 75° (c) 50° (d) 155°
  26. 26.Two angles of a triangle are 25° and 110°. What is the third angle? (a) 135° (b) 45° (c) 70° (d) 155°
  27. 27.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 115° (b) 85° (c) 160° (d) 95°
  28. 28.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 65° (b) 145° (c) 115° (d) 100°
  29. 29.Two angles of a triangle are 25° and 105°. What is the exterior angle at the third corner? (a) 50° (b) 155° (c) 75° (d) 130°
  30. 30.Two angles of a triangle are 60° and 55°. What is the exterior angle at the third corner? (a) 65° (b) 120° (c) 115° (d) 125°
  31. 31.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 61° (b) 120° (c) 60° (d) 240°
  32. 32.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 55° (b) 56° (c) 125° (d) 235°
  33. 33.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 35° (c) 55° (d) 70°
  34. 34.Two angles of a triangle are 60° and 20°. What is the third angle? (a) 120° (b) 160° (c) 80° (d) 100°
  35. 35.Two angles of a triangle are 45° and 25°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 155° (d) 135°
  36. 36.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 45° (c) 90° (d) 135°
  37. 37.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 45° (b) 110° (c) 135° (d) 115°
  38. 38.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 140° (b) 40° (c) 115° (d) 105°
  39. 39.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 55° (b) 110° (c) 70° (d) 20°
  40. 40.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 70° (c) 110° (d) 35°

Answer key

  1. 30°
  2. 15°
  3. 75°
  4. 10°
  5. 60°
  6. 90°
  7. 125°
  8. 120°
  9. 105°
  10. 55°
  11. 25°
  12. 25°
  13. 40°
  14. 20°
  15. 80°
  16. 125°
  17. 15°
  18. 120°
  19. 110°
  20. 115°
  21. 10°
  22. 105°
  23. 105°
  24. 30°
  25. 50°
  26. 45°
  27. 85°
  28. 65°
  29. 130°
  30. 115°
  31. 60°
  32. 55°
  33. 70°
  34. 100°
  35. 70°
  36. 90°
  37. 135°
  38. 40°
  39. 55°
  40. 35°

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