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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 297 · 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 45° and 55°. What is the exterior angle at the third corner? (a) 135° (b) 80° (c) 125° (d) 100°
  2. 2.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 110° (b) 165° (c) 15° (d) 85°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 80° (c) 40° (d) 100°
  4. 4.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) 55° (d) 90°
  5. 5.Two angles of a triangle are 25° and 80°. What is the third angle? (a) 105° (b) 100° (c) 75° (d) 155°
  6. 6.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 15° (b) 75° (c) 285° (d) 105°
  7. 7.Two angles of a triangle are 25° and 105°. What is the third angle? (a) 130° (b) 75° (c) 155° (d) 50°
  8. 8.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 65° (b) 35° (c) 150° (d) 145°
  9. 9.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 305° (b) 125° (c) 35° (d) 55°
  10. 10.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 90° (c) 91° (d) 45°
  11. 11.Two angles of a triangle are 65° and 95°. What is the third angle? (a) 160° (b) 115° (c) 20° (d) 85°
  12. 12.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 160° (b) 45° (c) 155° (d) 135°
  13. 13.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 50° (b) 110° (c) 120° (d) 130°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 25° (b) 130° (c) 155° (d) 310°
  15. 15.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 50° (b) 10° (c) 140° (d) 170°
  16. 16.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 155° (c) 65° (d) 25°
  17. 17.Two angles of a triangle are 55° and 110°. What is the third angle? (a) 70° (b) 125° (c) 15° (d) 165°
  18. 18.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) 320° (c) 140° (d) 40°
  19. 19.Two angles of a triangle are 25° and 135°. What is the third angle? (a) 160° (b) 155° (c) 20° (d) 45°
  20. 20.Two angles of a triangle are 45° and 105°. What is the third angle? (a) 135° (b) 150° (c) 75° (d) 30°
  21. 21.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 280° (c) 140° (d) 100°
  22. 22.Two angles of a triangle are 45° and 30°. What is the third angle? (a) 135° (b) 150° (c) 105° (d) 75°
  23. 23.Two angles of a triangle are 40° and 75°. What is the third angle? (a) 115° (b) 105° (c) 65° (d) 140°
  24. 24.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 45° (b) 46° (c) 225° (d) 135°
  25. 25.Two angles of a triangle are 55° and 40°. What is the exterior angle at the third corner? (a) 125° (b) 95° (c) 140° (d) 85°
  26. 26.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 105° (b) 145° (c) 75° (d) 110°
  27. 27.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 10° (b) 280° (c) 80° (d) 100°
  28. 28.Two angles of a triangle are 20° and 55°. What is the exterior angle at the third corner? (a) 160° (b) 75° (c) 125° (d) 105°
  29. 29.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) 300° (d) 120°
  30. 30.Two angles of a triangle are 35° and 55°. What is the third angle? (a) 90° (b) 270° (c) 125° (d) 145°
  31. 31.Two angles of a triangle are 35° and 130°. What is the third angle? (a) 165° (b) 50° (c) 15° (d) 145°
  32. 32.Two angles of a triangle are 20° and 65°. What is the third angle? (a) 95° (b) 115° (c) 85° (d) 160°
  33. 33.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 150° (c) 60° (d) 30°
  34. 34.Two angles of a triangle are 30° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 150° (c) 80° (d) 100°
  35. 35.Two angles of a triangle are 50° and 50°. What is the exterior angle at the third corner? (a) 260° (b) 100° (c) 80° (d) 130°
  36. 36.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 30° (c) 150° (d) 120°
  37. 37.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 105° (b) 125° (c) 75° (d) 160°
  38. 38.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 100° (b) 155° (c) 105° (d) 75°
  39. 39.Two angles of a triangle are 60° and 20°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 120° (d) 160°
  40. 40.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 150° (b) 80° (c) 130° (d) 100°

Answer key

  1. 100°
  2. 15°
  3. 40°
  4. 45°
  5. 75°
  6. 105°
  7. 50°
  8. 35°
  9. 125°
  10. 90°
  11. 20°
  12. 135°
  13. 130°
  14. 155°
  15. 10°
  16. 130°
  17. 15°
  18. 140°
  19. 20°
  20. 30°
  21. 140°
  22. 105°
  23. 65°
  24. 45°
  25. 95°
  26. 105°
  27. 100°
  28. 75°
  29. 120°
  30. 90°
  31. 15°
  32. 95°
  33. 75°
  34. 100°
  35. 100°
  36. 120°
  37. 75°
  38. 105°
  39. 80°
  40. 100°

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