← Angles and triangles lesson New set →

Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 979 · 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 70°. What is each of the other two angles? (a) 35° (b) 290° (c) 145° (d) 110°
  2. 2.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 105° (b) 75° (c) 135° (d) 120°
  3. 3.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 50° (c) 40° (d) 80°
  4. 4.Two angles of a triangle are 40° and 125°. What is the third angle? (a) 15° (b) 140° (c) 55° (d) 165°
  5. 5.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°
  6. 6.Two angles of a triangle are 30° and 80°. What is the third angle? (a) 100° (b) 150° (c) 70° (d) 110°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 70° (b) 110° (c) 71° (d) 140°
  8. 8.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 145° (d) 140°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 10° (c) 50° (d) 80°
  10. 10.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 150° (b) 31° (c) 30° (d) 210°
  11. 11.Two angles of a triangle are 30° and 140°. What is the third angle? (a) 170° (b) 10° (c) 40° (d) 150°
  12. 12.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 120° (c) 60° (d) 30°
  13. 13.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 70° (c) 45° (d) 110°
  14. 14.Two angles of a triangle are 35° and 25°. What is the third angle? (a) 60° (b) 145° (c) 120° (d) 155°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 80° (b) 160° (c) 81° (d) 100°
  16. 16.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 215° (b) 145° (c) 36° (d) 35°
  17. 17.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 85° (b) 120° (c) 95° (d) 145°
  18. 18.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) 165° (c) 15° (d) 16°
  19. 19.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 90° (b) 160° (c) 270° (d) 110°
  20. 20.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 10° (b) 11° (c) 160° (d) 20°
  21. 21.Two angles of a triangle are 45° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 55° (c) 135° (d) 125°
  22. 22.Two angles of a triangle are 25° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 100° (c) 80° (d) 155°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 240° (b) 121° (c) 60° (d) 120°
  24. 24.Two angles of a triangle are 55° and 50°. What is the third angle? (a) 75° (b) 130° (c) 125° (d) 105°
  25. 25.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 100° (c) 65° (d) 145°
  26. 26.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 120° (b) 85° (c) 155° (d) 95°
  27. 27.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 60° (b) 30° (c) 330° (d) 150°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 60° (b) 31° (c) 150° (d) 30°
  29. 29.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 145° (b) 35° (c) 100° (d) 115°
  30. 30.Two angles of a triangle are 25° and 95°. What is the third angle? (a) 85° (b) 60° (c) 120° (d) 155°
  31. 31.Two angles of a triangle are 75° and 60°. What is the third angle? (a) 105° (b) 120° (c) 135° (d) 45°
  32. 32.Two angles of a triangle are 25° and 80°. What is the third angle? (a) 100° (b) 75° (c) 155° (d) 105°
  33. 33.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 235° (c) 110° (d) 55°
  34. 34.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 145° (b) 160° (c) 125° (d) 55°
  35. 35.Two angles of a triangle are 35° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 145° (c) 65° (d) 115°
  36. 36.Two angles of a triangle are 45° and 70°. What is the third angle? (a) 115° (b) 110° (c) 135° (d) 65°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 10° (b) 170° (c) 11° (d) 20°
  38. 38.Two angles of a triangle are 70° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 110° (c) 135° (d) 45°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 15° (b) 165° (c) 16° (d) 30°
  40. 40.Two angles of a triangle are 20° and 95°. What is the third angle? (a) 160° (b) 115° (c) 65° (d) 85°

Answer key

  1. 145°
  2. 75°
  3. 80°
  4. 15°
  5. 75°
  6. 70°
  7. 70°
  8. 75°
  9. 50°
  10. 30°
  11. 10°
  12. 60°
  13. 35°
  14. 120°
  15. 80°
  16. 35°
  17. 95°
  18. 15°
  19. 90°
  20. 10°
  21. 125°
  22. 80°
  23. 120°
  24. 75°
  25. 115°
  26. 95°
  27. 150°
  28. 30°
  29. 145°
  30. 60°
  31. 45°
  32. 75°
  33. 125°
  34. 55°
  35. 65°
  36. 65°
  37. 10°
  38. 135°
  39. 15°
  40. 65°

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