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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 95 · 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 25° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 105° (c) 155° (d) 75°
  2. 2.Two angles of a triangle are 40° and 55°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 140° (d) 125°
  3. 3.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 150° (c) 120° (d) 30°
  4. 4.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 40° (c) 100° (d) 50°
  5. 5.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 75° (b) 255° (c) 105° (d) 76°
  6. 6.Two angles of a triangle are 60° and 45°. What is the exterior angle at the third corner? (a) 75° (b) 120° (c) 135° (d) 105°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 80° (c) 50° (d) 10°
  8. 8.Two angles of a triangle are 60° and 35°. What is the third angle? (a) 120° (b) 85° (c) 145° (d) 95°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 50° (b) 100° (c) 51° (d) 130°
  10. 10.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 70° (c) 45° (d) 110°
  11. 11.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 150° (b) 60° (c) 330° (d) 30°
  12. 12.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 125° (b) 55° (c) 160° (d) 145°
  13. 13.Two angles of a triangle are 30° and 135°. What is the third angle? (a) 15° (b) 150° (c) 165° (d) 45°
  14. 14.Two angles of a triangle are 40° and 90°. What is the exterior angle at the third corner? (a) 130° (b) 140° (c) 90° (d) 50°
  15. 15.Two angles of a triangle are 50° and 110°. What is the third angle? (a) 20° (b) 130° (c) 160° (d) 70°
  16. 16.Two angles of a triangle are 20° and 30°. What is the exterior angle at the third corner? (a) 160° (b) 150° (c) 50° (d) 130°
  17. 17.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 90° (b) 105° (c) 15° (d) 165°
  18. 18.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 55° (b) 305° (c) 35° (d) 125°
  19. 19.Two angles of a triangle are 25° and 65°. What is the third angle? (a) 90° (b) 115° (c) 270° (d) 155°
  20. 20.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 110° (d) 235°
  21. 21.Two angles of a triangle are 35° and 80°. What is the exterior angle at the third corner? (a) 65° (b) 145° (c) 100° (d) 115°
  22. 22.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 55° (c) 70° (d) 125°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 40° (b) 160° (c) 21° (d) 20°
  24. 24.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 120° (c) 60° (d) 30°
  25. 25.Two angles of a triangle are 40° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 220° (c) 40° (d) 140°
  26. 26.Two angles of a triangle are 35° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 145° (c) 115° (d) 65°
  27. 27.Two angles of a triangle are 80° and 90°. What is the third angle? (a) 170° (b) 10° (c) 90° (d) 100°
  28. 28.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 110° (b) 120° (c) 70° (d) 130°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 61° (b) 59° (c) 120° (d) 60°
  30. 30.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) 125° (c) 235° (d) 56°
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 55° (b) 125° (c) 56° (d) 110°
  32. 32.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 320° (b) 140° (c) 40° (d) 50°
  33. 33.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 45° (b) 315° (c) 136° (d) 135°
  34. 34.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 75° (b) 145° (c) 110° (d) 105°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 30° (b) 60° (c) 40° (d) 120°
  36. 36.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 60° (c) 75° (d) 150°
  37. 37.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 155° (b) 100° (c) 25° (d) 105°
  38. 38.Two angles of a triangle are 40° and 65°. What is the third angle? (a) 140° (b) 75° (c) 115° (d) 105°
  39. 39.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 55° (c) 46° (d) 90°
  40. 40.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 5° (b) 95° (c) 85° (d) 275°

Answer key

  1. 75°
  2. 95°
  3. 120°
  4. 100°
  5. 75°
  6. 105°
  7. 50°
  8. 85°
  9. 50°
  10. 35°
  11. 150°
  12. 55°
  13. 15°
  14. 130°
  15. 20°
  16. 50°
  17. 15°
  18. 125°
  19. 90°
  20. 125°
  21. 115°
  22. 70°
  23. 20°
  24. 60°
  25. 140°
  26. 65°
  27. 10°
  28. 70°
  29. 60°
  30. 55°
  31. 55°
  32. 140°
  33. 135°
  34. 75°
  35. 30°
  36. 75°
  37. 25°
  38. 75°
  39. 45°
  40. 95°

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