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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 130 · 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.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 55° (c) 20° (d) 70°
  2. 2.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 260° (b) 81° (c) 80° (d) 100°
  3. 3.Two angles of a triangle are 30° and 45°. What is the third angle? (a) 105° (b) 135° (c) 150° (d) 75°
  4. 4.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 30° (b) 150° (c) 100° (d) 110°
  5. 5.Two angles of a triangle are 40° and 95°. What is the exterior angle at the third corner? (a) 140° (b) 45° (c) 135° (d) 85°
  6. 6.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 120° (c) 60° (d) 150°
  7. 7.Two angles of a triangle are 40° and 95°. What is the third angle? (a) 135° (b) 140° (c) 85° (d) 45°
  8. 8.Two angles of a triangle are 40° and 75°. What is the exterior angle at the third corner? (a) 140° (b) 65° (c) 115° (d) 105°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 90° (c) 55° (d) 46°
  10. 10.Two angles of a triangle are 20° and 45°. What is the exterior angle at the third corner? (a) 65° (b) 135° (c) 115° (d) 160°
  11. 11.Two angles of a triangle are 20° and 110°. What is the exterior angle at the third corner? (a) 70° (b) 160° (c) 130° (d) 50°
  12. 12.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 45° (b) 95° (c) 135° (d) 130°
  13. 13.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 315° (b) 135° (c) 136° (d) 45°
  14. 14.Two angles of a triangle are 45° and 45°. What is the exterior angle at the third corner? (a) 91° (b) 135° (c) 270° (d) 90°
  15. 15.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 75° (c) 15° (d) 30°
  16. 16.Two angles of a triangle are 25° and 70°. What is the exterior angle at the third corner? (a) 155° (b) 85° (c) 95° (d) 110°
  17. 17.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 100° (b) 80° (c) 135° (d) 145°
  18. 18.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 110° (d) 235°
  19. 19.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 95° (d) 35°
  20. 20.Two angles of a triangle are 30° and 140°. What is the third angle? (a) 170° (b) 150° (c) 10° (d) 40°
  21. 21.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 110° (c) 80° (d) 100°
  22. 22.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 140° (b) 50° (c) 40° (d) 320°
  23. 23.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 60° (c) 61° (d) 120°
  24. 24.Two angles of a triangle are 30° and 110°. What is the exterior angle at the third corner? (a) 140° (b) 70° (c) 40° (d) 150°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 11° (c) 10° (d) 20°
  26. 26.Two angles of a triangle are 50° and 75°. What is the exterior angle at the third corner? (a) 125° (b) 55° (c) 130° (d) 105°
  27. 27.Two angles of a triangle are 30° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 100° (c) 80° (d) 150°
  28. 28.Two angles of a triangle are 50° and 115°. What is the third angle? (a) 130° (b) 165° (c) 15° (d) 65°
  29. 29.Two angles of a triangle are 40° and 55°. What is the third angle? (a) 85° (b) 140° (c) 95° (d) 125°
  30. 30.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°
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 71° (b) 140° (c) 110° (d) 70°
  32. 32.Two angles of a triangle are 75° and 60°. What is the exterior angle at the third corner? (a) 135° (b) 45° (c) 105° (d) 120°
  33. 33.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 145° (b) 100° (c) 35° (d) 115°
  34. 34.Two angles of a triangle are 20° and 50°. What is the third angle? (a) 70° (b) 160° (c) 110° (d) 130°
  35. 35.Two angles of a triangle are 25° and 20°. What is the third angle? (a) 45° (b) 160° (c) 135° (d) 155°
  36. 36.Two angles of a triangle are 40° and 80°. What is the third angle? (a) 100° (b) 140° (c) 60° (d) 120°
  37. 37.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°
  38. 38.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 255° (b) 76° (c) 75° (d) 105°
  39. 39.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 145° (d) 120°
  40. 40.Two angles of a triangle are 35° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 145° (c) 70° (d) 110°

Answer key

  1. 55°
  2. 80°
  3. 105°
  4. 150°
  5. 135°
  6. 120°
  7. 45°
  8. 115°
  9. 45°
  10. 65°
  11. 130°
  12. 45°
  13. 135°
  14. 90°
  15. 30°
  16. 95°
  17. 100°
  18. 125°
  19. 145°
  20. 10°
  21. 100°
  22. 140°
  23. 60°
  24. 140°
  25. 10°
  26. 125°
  27. 100°
  28. 15°
  29. 85°
  30. 35°
  31. 70°
  32. 135°
  33. 145°
  34. 110°
  35. 135°
  36. 60°
  37. 40°
  38. 75°
  39. 95°
  40. 110°

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