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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 442 · 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 80° and 50°. What is the exterior angle at the third corner? (a) 100° (b) 130° (c) 230° (d) 50°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 120° (c) 30° (d) 60°
  3. 3.Two angles of a triangle are 70° and 60°. What is the third angle? (a) 130° (b) 120° (c) 110° (d) 50°
  4. 4.Two angles of a triangle are 75° and 60°. What is the third angle? (a) 105° (b) 135° (c) 45° (d) 120°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 50° (c) 140° (d) 40°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 300° (b) 120° (c) 30° (d) 150°
  7. 7.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°
  8. 8.Two angles of a triangle are 60° and 95°. What is the third angle? (a) 120° (b) 155° (c) 85° (d) 25°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 20° (c) 70° (d) 80°
  10. 10.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 55° (b) 125° (c) 235° (d) 110°
  11. 11.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 120° (b) 145° (c) 155° (d) 60°
  12. 12.Two angles of a triangle are 80° and 85°. What is the third angle? (a) 95° (b) 165° (c) 15° (d) 100°
  13. 13.Two angles of a triangle are 75° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 140° (c) 105° (d) 40°
  14. 14.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 100° (b) 120° (c) 140° (d) 60°
  15. 15.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 25° (c) 65° (d) 50°
  16. 16.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°
  17. 17.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 61° (b) 120° (c) 59° (d) 60°
  18. 18.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 26° (b) 155° (c) 205° (d) 25°
  19. 19.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 90° (b) 270° (c) 145° (d) 125°
  20. 20.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 70° (b) 145° (c) 290° (d) 110°
  21. 21.Two angles of a triangle are 30° and 20°. What is the third angle? (a) 130° (b) 50° (c) 150° (d) 160°
  22. 22.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 50° (b) 20° (c) 150° (d) 160°
  23. 23.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 65° (b) 155° (c) 335° (d) 25°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 40° (b) 140° (c) 80° (d) 41°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 70° (c) 20° (d) 55°
  26. 26.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 16° (b) 15° (c) 165° (d) 195°
  27. 27.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) 125° (c) 305° (d) 35°
  28. 28.Two angles of a triangle are 20° and 105°. What is the third angle? (a) 75° (b) 160° (c) 125° (d) 55°
  29. 29.Two angles of a triangle are 60° and 70°. What is the third angle? (a) 110° (b) 130° (c) 50° (d) 120°
  30. 30.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 15° (c) 25° (d) 150°
  31. 31.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 150° (b) 65° (c) 145° (d) 35°
  32. 32.Two angles of a triangle are 45° and 65°. What is the exterior angle at the third corner? (a) 70° (b) 135° (c) 115° (d) 110°
  33. 33.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 30° (c) 75° (d) 150°
  34. 34.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 105° (b) 110° (c) 35° (d) 145°
  35. 35.Two angles of a triangle are 25° and 75°. What is the third angle? (a) 105° (b) 80° (c) 100° (d) 155°
  36. 36.Two angles of a triangle are 80° and 70°. What is the third angle? (a) 110° (b) 100° (c) 150° (d) 30°
  37. 37.Two angles of a triangle are 45° and 35°. What is the third angle? (a) 145° (b) 80° (c) 135° (d) 100°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 50° (c) 40° (d) 80°
  39. 39.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 190° (b) 10° (c) 170° (d) 11°
  40. 40.Two angles of a triangle are 30° and 50°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 150° (d) 130°

Answer key

  1. 130°
  2. 30°
  3. 50°
  4. 45°
  5. 70°
  6. 150°
  7. 140°
  8. 25°
  9. 80°
  10. 55°
  11. 120°
  12. 15°
  13. 140°
  14. 120°
  15. 50°
  16. 110°
  17. 60°
  18. 25°
  19. 90°
  20. 70°
  21. 130°
  22. 20°
  23. 155°
  24. 40°
  25. 55°
  26. 15°
  27. 125°
  28. 55°
  29. 50°
  30. 15°
  31. 35°
  32. 110°
  33. 75°
  34. 35°
  35. 80°
  36. 30°
  37. 100°
  38. 40°
  39. 10°
  40. 80°

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