← Angles and triangles lesson New set →

Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 402 · 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 70° and 60°. What is the third angle? (a) 120° (b) 110° (c) 50° (d) 130°
  2. 2.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 35° (b) 145° (c) 110° (d) 105°
  3. 3.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 115° (c) 25° (d) 50°
  4. 4.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 140° (c) 40° (d) 100°
  5. 5.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 210° (b) 31° (c) 30° (d) 150°
  6. 6.Two angles of a triangle are 50° and 20°. What is the third angle? (a) 70° (b) 110° (c) 130° (d) 160°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 150° (c) 75° (d) 60°
  8. 8.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°
  9. 9.Two angles of a triangle are 55° and 75°. What is the third angle? (a) 130° (b) 50° (c) 105° (d) 125°
  10. 10.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 195° (b) 16° (c) 15° (d) 165°
  11. 11.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 60° (c) 120° (d) 150°
  12. 12.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 130° (b) 45° (c) 95° (d) 135°
  13. 13.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 275° (b) 85° (c) 5° (d) 95°
  14. 14.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 230° (b) 51° (c) 130° (d) 50°
  15. 15.Two angles of a triangle are 45° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 225° (c) 135° (d) 45°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 155° (b) 26° (c) 25° (d) 50°
  17. 17.Two angles of a triangle are 20° and 110°. What is the exterior angle at the third corner? (a) 160° (b) 130° (c) 70° (d) 50°
  18. 18.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 130° (d) 160°
  19. 19.Two angles of a triangle are 65° and 65°. What is the third angle? (a) 50° (b) 115° (c) 230° (d) 130°
  20. 20.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 100° (c) 50° (d) 10°
  21. 21.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 120° (b) 130° (c) 70° (d) 110°
  22. 22.Two angles of a triangle are 40° and 115°. What is the third angle? (a) 140° (b) 65° (c) 155° (d) 25°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 160° (b) 21° (c) 20° (d) 40°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 41° (b) 80° (c) 40° (d) 140°
  25. 25.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 15° (b) 165° (c) 85° (d) 110°
  26. 26.Two angles of a triangle are 35° and 120°. What is the third angle? (a) 60° (b) 145° (c) 155° (d) 25°
  27. 27.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 155° (b) 205° (c) 26° (d) 25°
  28. 28.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 105° (b) 170° (c) 85° (d) 10°
  29. 29.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 155° (d) 100°
  30. 30.Two angles of a triangle are 40° and 40°. What is the exterior angle at the third corner? (a) 100° (b) 280° (c) 80° (d) 140°
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 95° (c) 86° (d) 85°
  32. 32.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 10° (c) 80° (d) 20°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 80° (c) 260° (d) 130°
  34. 34.Two angles of a triangle are 30° and 45°. What is the third angle? (a) 105° (b) 135° (c) 75° (d) 150°
  35. 35.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 10° (c) 85° (d) 5°
  36. 36.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 46° (c) 45° (d) 55°
  37. 37.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 130° (b) 125° (c) 55° (d) 105°
  38. 38.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 85° (c) 95° (d) 120°
  39. 39.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 125° (b) 55° (c) 155° (d) 150°
  40. 40.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 25° (c) 150° (d) 15°

Answer key

  1. 50°
  2. 35°
  3. 50°
  4. 100°
  5. 30°
  6. 110°
  7. 75°
  8. 135°
  9. 50°
  10. 15°
  11. 120°
  12. 45°
  13. 95°
  14. 50°
  15. 135°
  16. 25°
  17. 130°
  18. 70°
  19. 50°
  20. 50°
  21. 70°
  22. 25°
  23. 20°
  24. 40°
  25. 15°
  26. 25°
  27. 25°
  28. 10°
  29. 105°
  30. 80°
  31. 85°
  32. 20°
  33. 130°
  34. 105°
  35. 10°
  36. 45°
  37. 55°
  38. 95°
  39. 55°
  40. 15°

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