← Angles and triangles lesson New set →

Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 571 · 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. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 260° (b) 50° (c) 80° (d) 130°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 30° (c) 60° (d) 75°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 120° (c) 70° (d) 60°
  4. 4.Two angles of a triangle are 60° and 30°. What is the exterior angle at the third corner? (a) 270° (b) 150° (c) 120° (d) 90°
  5. 5.Two angles of a triangle are 65° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 115° (c) 95° (d) 85°
  6. 6.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 30° (c) 60° (d) 61°
  7. 7.Two angles of a triangle are 80° and 55°. What is the third angle? (a) 135° (b) 125° (c) 45° (d) 100°
  8. 8.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 265° (c) 85° (d) 95°
  9. 9.Two angles of a triangle are 55° and 90°. What is the third angle? (a) 35° (b) 145° (c) 125° (d) 90°
  10. 10.Two angles of a triangle are 30° and 65°. What is the third angle? (a) 115° (b) 150° (c) 95° (d) 85°
  11. 11.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) 45° (d) 35°
  12. 12.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 30° (c) 75° (d) 15°
  13. 13.Two angles of a triangle are 25° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 155° (c) 100° (d) 80°
  14. 14.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 130° (b) 70° (c) 120° (d) 110°
  15. 15.Two angles of a triangle are 55° and 65°. What is the exterior angle at the third corner? (a) 60° (b) 115° (c) 125° (d) 120°
  16. 16.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 80° (c) 130° (d) 100°
  17. 17.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 120° (b) 60° (c) 40° (d) 30°
  18. 18.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 120° (b) 130° (c) 110° (d) 60°
  19. 19.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 150° (b) 270° (c) 120° (d) 90°
  20. 20.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 105° (b) 75° (c) 15° (d) 285°
  21. 21.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 135° (d) 150°
  22. 22.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 155° (c) 65° (d) 130°
  23. 23.Two angles of a triangle are 45° and 90°. What is the third angle? (a) 225° (b) 90° (c) 45° (d) 135°
  24. 24.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 125° (b) 155° (c) 25° (d) 80°
  25. 25.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 145° (b) 110° (c) 105° (d) 75°
  26. 26.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 30° (c) 20° (d) 140°
  27. 27.Two angles of a triangle are 55° and 50°. What is the third angle? (a) 105° (b) 75° (c) 130° (d) 125°
  28. 28.Two angles of a triangle are 20° and 85°. What is the third angle? (a) 95° (b) 75° (c) 105° (d) 160°
  29. 29.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 15° (c) 150° (d) 25°
  30. 30.Two angles of a triangle are 45° and 25°. What is the exterior angle at the third corner? (a) 70° (b) 135° (c) 155° (d) 110°
  31. 31.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 70° (c) 55° (d) 125°
  32. 32.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 20° (c) 10° (d) 100°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 30° (b) 105° (c) 75° (d) 210°
  34. 34.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 155° (b) 135° (c) 45° (d) 160°
  35. 35.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 205° (b) 25° (c) 155° (d) 26°
  36. 36.Two angles of a triangle are 35° and 75°. What is the third angle? (a) 110° (b) 70° (c) 145° (d) 105°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 85° (b) 10° (c) 95° (d) 190°
  38. 38.Two angles of a triangle are 75° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 130° (c) 105° (d) 50°
  39. 39.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 150° (b) 105° (c) 210° (d) 30°
  40. 40.Two angles of a triangle are 50° and 50°. What is the third angle? (a) 260° (b) 100° (c) 80° (d) 130°

Answer key

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

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