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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 154 · 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. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 15° (b) 165° (c) 16° (d) 195°
  2. 2.Two angles of a triangle are 35° and 95°. What is the exterior angle at the third corner? (a) 145° (b) 130° (c) 50° (d) 85°
  3. 3.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 145° (b) 35° (c) 65° (d) 150°
  4. 4.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 70° (c) 35° (d) 45°
  5. 5.Two angles of a triangle are 65° and 30°. What is the exterior angle at the third corner? (a) 115° (b) 150° (c) 95° (d) 85°
  6. 6.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 160° (c) 11° (d) 10°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 80° (b) 160° (c) 70° (d) 20°
  8. 8.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 46° (b) 45° (c) 135° (d) 90°
  9. 9.Two angles of a triangle are 20° and 75°. What is the third angle? (a) 85° (b) 95° (c) 105° (d) 160°
  10. 10.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 80° (c) 130° (d) 40°
  11. 11.Two angles of a triangle are 55° and 55°. What is the exterior angle at the third corner? (a) 70° (b) 250° (c) 110° (d) 125°
  12. 12.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 90° (b) 145° (c) 125° (d) 270°
  13. 13.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 115° (b) 145° (c) 35° (d) 100°
  14. 14.Two angles of a triangle are 35° and 125°. What is the third angle? (a) 55° (b) 160° (c) 145° (d) 20°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 60° (c) 30° (d) 70°
  16. 16.Two angles of a triangle are 55° and 45°. What is the exterior angle at the third corner? (a) 80° (b) 125° (c) 135° (d) 100°
  17. 17.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°
  18. 18.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 135° (c) 91° (d) 90°
  19. 19.Two angles of a triangle are 80° and 50°. What is the exterior angle at the third corner? (a) 50° (b) 230° (c) 100° (d) 130°
  20. 20.Two angles of a triangle are 30° and 95°. What is the exterior angle at the third corner? (a) 150° (b) 55° (c) 125° (d) 85°
  21. 21.Two angles of a triangle are 75° and 85°. What is the third angle? (a) 105° (b) 160° (c) 95° (d) 20°
  22. 22.Two angles of a triangle are 45° and 25°. What is the exterior angle at the third corner? (a) 135° (b) 155° (c) 110° (d) 70°
  23. 23.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 100° (b) 75° (c) 105° (d) 155°
  24. 24.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 125° (b) 135° (c) 100° (d) 45°
  25. 25.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 145° (b) 100° (c) 35° (d) 115°
  26. 26.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 25° (b) 115° (c) 295° (d) 65°
  27. 27.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 135° (b) 270° (c) 45° (d) 90°
  28. 28.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 140° (b) 105° (c) 115° (d) 40°
  29. 29.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 45° (b) 100° (c) 125° (d) 135°
  30. 30.Two angles of a triangle are 60° and 80°. What is the exterior angle at the third corner? (a) 140° (b) 120° (c) 40° (d) 100°
  31. 31.Two angles of a triangle are 50° and 45°. What is the third angle? (a) 85° (b) 95° (c) 135° (d) 130°
  32. 32.Two angles of a triangle are 20° and 55°. What is the exterior angle at the third corner? (a) 160° (b) 105° (c) 125° (d) 75°
  33. 33.Two angles of a triangle are 25° and 30°. What is the third angle? (a) 55° (b) 150° (c) 155° (d) 125°
  34. 34.Two angles of a triangle are 55° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 125° (c) 85° (d) 95°
  35. 35.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 60° (b) 155° (c) 145° (d) 120°
  36. 36.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 125° (b) 55° (c) 235° (d) 56°
  37. 37.Two angles of a triangle are 35° and 105°. What is the third angle? (a) 75° (b) 40° (c) 140° (d) 145°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 60° (b) 121° (c) 240° (d) 120°
  39. 39.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 15° (c) 150° (d) 30°
  40. 40.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 270° (b) 160° (c) 90° (d) 110°

Answer key

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

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