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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 315 · 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 65° and 20°. What is the third angle? (a) 85° (b) 95° (c) 160° (d) 115°
  2. 2.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 50° (c) 115° (d) 65°
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 110° (b) 56° (c) 55° (d) 125°
  4. 4.Two angles of a triangle are 30° and 120°. What is the exterior angle at the third corner? (a) 150° (b) 60° (c) 30° (d) 210°
  5. 5.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 55° (c) 35° (d) 110°
  6. 6.Two angles of a triangle are 30° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 95° (c) 85° (d) 150°
  7. 7.Two angles of a triangle are 40° and 70°. What is the third angle? (a) 250° (b) 140° (c) 110° (d) 70°
  8. 8.Two angles of a triangle are 40° and 100°. What is the third angle? (a) 220° (b) 80° (c) 140° (d) 40°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 26° (b) 25° (c) 155° (d) 50°
  10. 10.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 65° (b) 25° (c) 115° (d) 295°
  11. 11.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 40° (c) 20° (d) 110°
  12. 12.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 65° (c) 155° (d) 130°
  13. 13.Two angles of a triangle are 30° and 95°. What is the third angle? (a) 85° (b) 150° (c) 55° (d) 125°
  14. 14.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 25° (b) 205° (c) 26° (d) 155°
  15. 15.Two angles of a triangle are 60° and 60°. What is the third angle? (a) 240° (b) 120° (c) 61° (d) 60°
  16. 16.Two angles of a triangle are 60° and 30°. What is the exterior angle at the third corner? (a) 90° (b) 270° (c) 150° (d) 120°
  17. 17.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 105° (b) 145° (c) 140° (d) 75°
  18. 18.Two angles of a triangle are 50° and 105°. What is the third angle? (a) 155° (b) 130° (c) 75° (d) 25°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 130° (c) 65° (d) 50°
  20. 20.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 75° (b) 130° (c) 105° (d) 155°
  21. 21.Two angles of a triangle are 60° and 85°. What is the third angle? (a) 120° (b) 35° (c) 95° (d) 145°
  22. 22.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 40° (c) 130° (d) 50°
  23. 23.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) 61° (c) 60° (d) 120°
  24. 24.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 50° (c) 130° (d) 230°
  25. 25.Two angles of a triangle are 25° and 145°. What is the third angle? (a) 170° (b) 35° (c) 10° (d) 155°
  26. 26.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) 105° (d) 75°
  27. 27.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 100° (c) 65° (d) 115°
  28. 28.Two angles of a triangle are 65° and 55°. What is the exterior angle at the third corner? (a) 60° (b) 115° (c) 125° (d) 120°
  29. 29.Two angles of a triangle are 55° and 25°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 125° (d) 155°
  30. 30.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 150° (b) 85° (c) 95° (d) 115°
  31. 31.Two angles of a triangle are 30° and 110°. What is the exterior angle at the third corner? (a) 150° (b) 40° (c) 70° (d) 140°
  32. 32.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) 290° (c) 20° (d) 110°
  33. 33.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 145° (b) 35° (c) 100° (d) 115°
  34. 34.Two angles of a triangle are 20° and 125°. What is the exterior angle at the third corner? (a) 35° (b) 160° (c) 145° (d) 55°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 140° (b) 70° (c) 110° (d) 71°
  36. 36.Two angles of a triangle are 70° and 45°. What is the third angle? (a) 115° (b) 65° (c) 110° (d) 135°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 100° (b) 51° (c) 50° (d) 130°
  38. 38.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 60° (c) 120° (d) 30°
  39. 39.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°
  40. 40.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 115° (b) 145° (c) 100° (d) 35°

Answer key

  1. 95°
  2. 50°
  3. 55°
  4. 150°
  5. 110°
  6. 95°
  7. 70°
  8. 40°
  9. 25°
  10. 115°
  11. 40°
  12. 130°
  13. 55°
  14. 25°
  15. 60°
  16. 90°
  17. 105°
  18. 25°
  19. 65°
  20. 75°
  21. 35°
  22. 80°
  23. 60°
  24. 130°
  25. 10°
  26. 75°
  27. 115°
  28. 120°
  29. 80°
  30. 85°
  31. 140°
  32. 110°
  33. 145°
  34. 145°
  35. 70°
  36. 65°
  37. 50°
  38. 60°
  39. 130°
  40. 145°

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