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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 426 · 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 35° and 30°. What is the exterior angle at the third corner? (a) 145° (b) 115° (c) 65° (d) 150°
  2. 2.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 105° (b) 76° (c) 255° (d) 75°
  3. 3.Two angles of a triangle are 45° and 125°. What is the third angle? (a) 55° (b) 170° (c) 10° (d) 135°
  4. 4.Two angles of a triangle are 25° and 90°. What is the exterior angle at the third corner? (a) 65° (b) 90° (c) 115° (d) 155°
  5. 5.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 55° (b) 145° (c) 35° (d) 325°
  6. 6.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 260° (b) 80° (c) 100° (d) 160°
  7. 7.Two angles of a triangle are 25° and 70°. What is the exterior angle at the third corner? (a) 95° (b) 110° (c) 155° (d) 85°
  8. 8.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 80° (c) 50° (d) 40°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 100° (c) 140° (d) 280°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 150° (b) 120° (c) 300° (d) 30°
  11. 11.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) 120° (d) 300°
  12. 12.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 35° (b) 150° (c) 65° (d) 145°
  13. 13.Two angles of a triangle are 40° and 115°. What is the third angle? (a) 65° (b) 155° (c) 25° (d) 140°
  14. 14.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 130° (b) 145° (c) 95° (d) 85°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 30° (c) 20° (d) 140°
  16. 16.Two angles of a triangle are 70° and 90°. What is the third angle? (a) 20° (b) 110° (c) 160° (d) 90°
  17. 17.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 130° (c) 260° (d) 80°
  18. 18.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 120° (b) 60° (c) 61° (d) 59°
  19. 19.Two angles of a triangle are 65° and 75°. What is the third angle? (a) 40° (b) 140° (c) 105° (d) 115°
  20. 20.Two angles of a triangle are 50° and 25°. What is the third angle? (a) 155° (b) 105° (c) 75° (d) 130°
  21. 21.Two angles of a triangle are 50° and 80°. What is the third angle? (a) 100° (b) 230° (c) 130° (d) 50°
  22. 22.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 130° (c) 110° (d) 70°
  23. 23.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 100° (b) 80° (c) 135° (d) 125°
  24. 24.Two angles of a triangle are 25° and 115°. What is the third angle? (a) 140° (b) 40° (c) 65° (d) 155°
  25. 25.Two angles of a triangle are 65° and 105°. What is the third angle? (a) 10° (b) 170° (c) 75° (d) 115°
  26. 26.Two angles of a triangle are 30° and 60°. What is the third angle? (a) 120° (b) 150° (c) 90° (d) 270°
  27. 27.Two angles of a triangle are 45° and 90°. What is the third angle? (a) 45° (b) 90° (c) 135° (d) 225°
  28. 28.Two angles of a triangle are 50° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 140° (c) 130° (d) 40°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 20° (b) 10° (c) 11° (d) 170°
  30. 30.Two angles of a triangle are 60° and 20°. What is the third angle? (a) 80° (b) 120° (c) 160° (d) 100°
  31. 31.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 86° (c) 85° (d) 265°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 70° (c) 20° (d) 80°
  33. 33.Two angles of a triangle are 55° and 25°. What is the exterior angle at the third corner? (a) 80° (b) 125° (c) 100° (d) 155°
  34. 34.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 10° (b) 160° (c) 20° (d) 11°
  35. 35.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 155° (c) 25° (d) 130°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 250° (b) 70° (c) 125° (d) 55°
  37. 37.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 75° (c) 105° (d) 130°
  38. 38.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 160° (b) 125° (c) 55° (d) 145°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 15° (b) 165° (c) 30° (d) 16°
  40. 40.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 35° (b) 305° (c) 55° (d) 125°

Answer key

  1. 65°
  2. 75°
  3. 10°
  4. 115°
  5. 145°
  6. 100°
  7. 95°
  8. 80°
  9. 140°
  10. 150°
  11. 120°
  12. 35°
  13. 25°
  14. 85°
  15. 20°
  16. 20°
  17. 130°
  18. 60°
  19. 40°
  20. 105°
  21. 50°
  22. 70°
  23. 80°
  24. 40°
  25. 10°
  26. 90°
  27. 45°
  28. 140°
  29. 10°
  30. 100°
  31. 85°
  32. 80°
  33. 80°
  34. 10°
  35. 130°
  36. 125°
  37. 75°
  38. 125°
  39. 15°
  40. 125°

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