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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 226 · 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 70° and 85°. What is the third angle? (a) 95° (b) 110° (c) 155° (d) 25°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 80° (c) 70° (d) 160°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 45° (c) 55° (d) 90°
  4. 4.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 55° (b) 20° (c) 70° (d) 110°
  5. 5.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 75° (b) 105° (c) 140° (d) 145°
  6. 6.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 50° (c) 100° (d) 80°
  7. 7.Two angles of a triangle are 45° and 50°. What is the third angle? (a) 130° (b) 135° (c) 95° (d) 85°
  8. 8.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 70° (b) 110° (c) 20° (d) 290°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 110° (c) 35° (d) 70°
  10. 10.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 76° (b) 255° (c) 75° (d) 105°
  11. 11.Two angles of a triangle are 65° and 50°. What is the third angle? (a) 115° (b) 65° (c) 130° (d) 245°
  12. 12.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 120° (b) 85° (c) 95° (d) 155°
  13. 13.Two angles of a triangle are 40° and 85°. What is the third angle? (a) 140° (b) 125° (c) 95° (d) 55°
  14. 14.Two angles of a triangle are 20° and 95°. What is the exterior angle at the third corner? (a) 65° (b) 85° (c) 115° (d) 160°
  15. 15.Two angles of a triangle are 30° and 95°. What is the third angle? (a) 150° (b) 125° (c) 85° (d) 55°
  16. 16.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 45° (b) 135° (c) 155° (d) 160°
  17. 17.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 115° (c) 95° (d) 85°
  18. 18.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 125° (b) 105° (c) 55° (d) 130°
  19. 19.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 240° (b) 60° (c) 61° (d) 120°
  20. 20.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 105° (b) 140° (c) 75° (d) 145°
  21. 21.Two angles of a triangle are 65° and 70°. What is the third angle? (a) 45° (b) 115° (c) 110° (d) 135°
  22. 22.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 50° (c) 100° (d) 140°
  23. 23.Two angles of a triangle are 70° and 80°. What is the third angle? (a) 100° (b) 30° (c) 110° (d) 150°
  24. 24.Two angles of a triangle are 35° and 70°. What is the third angle? (a) 105° (b) 110° (c) 145° (d) 75°
  25. 25.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 170° (b) 190° (c) 10° (d) 11°
  26. 26.Two angles of a triangle are 60° and 100°. What is the third angle? (a) 120° (b) 160° (c) 80° (d) 20°
  27. 27.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 265° (c) 95° (d) 86°
  28. 28.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 65° (c) 50° (d) 40°
  29. 29.Two angles of a triangle are 40° and 90°. What is the exterior angle at the third corner? (a) 140° (b) 50° (c) 130° (d) 90°
  30. 30.Two angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 115° (b) 155° (c) 65° (d) 140°
  31. 31.Two angles of a triangle are 45° and 50°. What is the exterior angle at the third corner? (a) 95° (b) 130° (c) 135° (d) 85°
  32. 32.Two angles of a triangle are 20° and 80°. What is the third angle? (a) 100° (b) 80° (c) 160° (d) 260°
  33. 33.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 50° (b) 310° (c) 40° (d) 130°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 86° (c) 95° (d) 170°
  35. 35.Two angles of a triangle are 40° and 80°. What is the third angle? (a) 140° (b) 100° (c) 60° (d) 120°
  36. 36.Two angles of a triangle are 80° and 45°. What is the exterior angle at the third corner? (a) 55° (b) 100° (c) 135° (d) 125°
  37. 37.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°
  38. 38.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 130° (b) 135° (c) 45° (d) 95°
  39. 39.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 140° (c) 20° (d) 30°
  40. 40.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 165° (b) 16° (c) 15° (d) 195°

Answer key

  1. 25°
  2. 80°
  3. 45°
  4. 55°
  5. 105°
  6. 40°
  7. 85°
  8. 110°
  9. 35°
  10. 75°
  11. 65°
  12. 95°
  13. 55°
  14. 115°
  15. 55°
  16. 135°
  17. 85°
  18. 125°
  19. 60°
  20. 75°
  21. 45°
  22. 100°
  23. 30°
  24. 75°
  25. 10°
  26. 20°
  27. 85°
  28. 65°
  29. 130°
  30. 65°
  31. 95°
  32. 80°
  33. 130°
  34. 85°
  35. 60°
  36. 125°
  37. 85°
  38. 45°
  39. 20°
  40. 15°

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