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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 82 · 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 straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 50° (b) 51° (c) 100° (d) 130°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 15° (b) 30° (c) 25° (d) 150°
  3. 3.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°
  4. 4.Two angles of a triangle are 35° and 20°. What is the third angle? (a) 55° (b) 160° (c) 125° (d) 145°
  5. 5.Two angles of a triangle are 45° and 40°. What is the third angle? (a) 140° (b) 95° (c) 85° (d) 135°
  6. 6.Two angles of a triangle are 35° and 100°. What is the exterior angle at the third corner? (a) 45° (b) 145° (c) 135° (d) 80°
  7. 7.Two angles of a triangle are 20° and 30°. What is the exterior angle at the third corner? (a) 130° (b) 160° (c) 150° (d) 50°
  8. 8.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 290° (b) 145° (c) 70° (d) 110°
  9. 9.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 15° (c) 75° (d) 30°
  10. 10.Two angles of a triangle are 25° and 135°. What is the third angle? (a) 155° (b) 160° (c) 45° (d) 20°
  11. 11.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 80° (b) 160° (c) 260° (d) 100°
  12. 12.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 20° (b) 21° (c) 160° (d) 200°
  13. 13.Two angles of a triangle are 60° and 100°. What is the third angle? (a) 20° (b) 160° (c) 80° (d) 120°
  14. 14.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 95° (c) 86° (d) 85°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 50° (c) 40° (d) 70°
  16. 16.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 40° (b) 155° (c) 15° (d) 165°
  17. 17.Two angles of a triangle are 45° and 125°. What is the third angle? (a) 170° (b) 55° (c) 10° (d) 135°
  18. 18.Two angles of a triangle are 25° and 100°. What is the exterior angle at the third corner? (a) 55° (b) 80° (c) 125° (d) 155°
  19. 19.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 40° (c) 130° (d) 50°
  20. 20.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 235° (b) 55° (c) 125° (d) 56°
  21. 21.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 25° (b) 65° (c) 335° (d) 155°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 145° (b) 35° (c) 110° (d) 290°
  23. 23.Two angles of a triangle are 75° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 45° (c) 135° (d) 105°
  24. 24.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 95° (b) 85° (c) 5° (d) 275°
  25. 25.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 160° (b) 80° (c) 100° (d) 81°
  26. 26.Two angles of a triangle are 50° and 95°. What is the exterior angle at the third corner? (a) 145° (b) 130° (c) 85° (d) 35°
  27. 27.Two angles of a triangle are 30° and 40°. What is the exterior angle at the third corner? (a) 110° (b) 150° (c) 140° (d) 70°
  28. 28.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 30° (b) 95° (c) 115° (d) 150°
  29. 29.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 90° (b) 125° (c) 270° (d) 145°
  30. 30.Two angles of a triangle are 60° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 120° (c) 50° (d) 130°
  31. 31.Two angles of a triangle are 20° and 120°. What is the third angle? (a) 160° (b) 140° (c) 60° (d) 40°
  32. 32.Two angles of a triangle are 65° and 85°. What is the third angle? (a) 115° (b) 30° (c) 150° (d) 95°
  33. 33.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 140° (b) 100° (c) 80° (d) 120°
  34. 34.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°
  35. 35.Two angles of a triangle are 70° and 70°. What is the third angle? (a) 140° (b) 40° (c) 220° (d) 110°
  36. 36.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 90° (b) 270° (c) 155° (d) 115°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 135° (b) 90° (c) 46° (d) 45°
  38. 38.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 160° (c) 70° (d) 340°
  39. 39.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 41° (b) 140° (c) 220° (d) 40°
  40. 40.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 65° (c) 25° (d) 155°

Answer key

  1. 50°
  2. 15°
  3. 75°
  4. 125°
  5. 95°
  6. 135°
  7. 50°
  8. 70°
  9. 30°
  10. 20°
  11. 100°
  12. 20°
  13. 20°
  14. 85°
  15. 70°
  16. 15°
  17. 10°
  18. 125°
  19. 80°
  20. 55°
  21. 155°
  22. 145°
  23. 135°
  24. 95°
  25. 80°
  26. 145°
  27. 70°
  28. 150°
  29. 90°
  30. 130°
  31. 40°
  32. 30°
  33. 80°
  34. 45°
  35. 40°
  36. 90°
  37. 45°
  38. 160°
  39. 40°
  40. 130°

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