← Angles and triangles lesson New set →

Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 54 · 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 55° and 50°. What is the third angle? (a) 125° (b) 105° (c) 130° (d) 75°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 140° (c) 20° (d) 40°
  3. 3.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 145° (b) 325° (c) 35° (d) 55°
  4. 4.Two angles of a triangle are 25° and 30°. What is the exterior angle at the third corner? (a) 155° (b) 55° (c) 125° (d) 150°
  5. 5.Two angles of a triangle are 60° and 20°. What is the third angle? (a) 80° (b) 120° (c) 100° (d) 160°
  6. 6.Two angles of a triangle are 70° and 90°. What is the third angle? (a) 160° (b) 90° (c) 20° (d) 110°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 25° (c) 50° (d) 35°
  8. 8.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 125° (b) 55° (c) 150° (d) 155°
  9. 9.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 60° (c) 30° (d) 120°
  10. 10.Two angles of a triangle are 40° and 80°. What is the third angle? (a) 60° (b) 100° (c) 140° (d) 120°
  11. 11.Two angles of a triangle are 70° and 75°. What is the exterior angle at the third corner? (a) 145° (b) 110° (c) 105° (d) 35°
  12. 12.Two angles of a triangle are 30° and 60°. What is the exterior angle at the third corner? (a) 90° (b) 150° (c) 270° (d) 120°
  13. 13.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 155° (c) 75° (d) 105°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 55° (c) 46° (d) 45°
  15. 15.Two angles of a triangle are 55° and 35°. What is the exterior angle at the third corner? (a) 125° (b) 145° (c) 90° (d) 270°
  16. 16.Two angles of a triangle are 20° and 150°. What is the third angle? (a) 160° (b) 10° (c) 170° (d) 30°
  17. 17.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 105° (b) 25° (c) 155° (d) 100°
  18. 18.Two angles of a triangle are 25° and 70°. What is the third angle? (a) 95° (b) 110° (c) 155° (d) 85°
  19. 19.Two angles of a triangle are 55° and 55°. What is the exterior angle at the third corner? (a) 110° (b) 250° (c) 125° (d) 70°
  20. 20.Two angles of a triangle are 20° and 140°. What is the third angle? (a) 40° (b) 20° (c) 160° (d) 200°
  21. 21.Two angles of a triangle are 35° and 60°. What is the third angle? (a) 95° (b) 145° (c) 120° (d) 85°
  22. 22.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 105° (b) 35° (c) 145° (d) 110°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 90° (b) 135° (c) 45° (d) 46°
  24. 24.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 10° (c) 85° (d) 95°
  25. 25.Two angles of a triangle are 20° and 75°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 105° (d) 160°
  26. 26.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 105° (b) 75° (c) 135° (d) 120°
  27. 27.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 100° (c) 40° (d) 140°
  28. 28.Two angles of a triangle are 20° and 90°. What is the third angle? (a) 90° (b) 70° (c) 160° (d) 110°
  29. 29.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 155° (b) 105° (c) 80° (d) 100°
  30. 30.Two angles of a triangle are 45° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 65° (c) 115° (d) 135°
  31. 31.Two angles of a triangle are 35° and 70°. What is the third angle? (a) 145° (b) 105° (c) 75° (d) 110°
  32. 32.Two angles of a triangle are 70° and 85°. What is the third angle? (a) 25° (b) 95° (c) 110° (d) 155°
  33. 33.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 125° (c) 55° (d) 150°
  34. 34.Two angles of a triangle are 35° and 120°. What is the third angle? (a) 155° (b) 25° (c) 60° (d) 145°
  35. 35.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 235° (b) 110° (c) 55° (d) 125°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 110° (b) 70° (c) 71° (d) 140°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 120° (b) 240° (c) 60° (d) 121°
  38. 38.Two angles of a triangle are 80° and 90°. What is the third angle? (a) 10° (b) 100° (c) 170° (d) 90°
  39. 39.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 110° (c) 40° (d) 20°
  40. 40.Two angles of a triangle are 25° and 95°. What is the exterior angle at the third corner? (a) 155° (b) 60° (c) 85° (d) 120°

Answer key

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

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad