← Angles and triangles lesson New set →

Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 488 · 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 30°. What is the exterior angle at the third corner? (a) 150° (b) 95° (c) 125° (d) 85°
  2. 2.Two angles of a triangle are 35° and 130°. What is the third angle? (a) 145° (b) 50° (c) 165° (d) 15°
  3. 3.Two angles of a triangle are 65° and 60°. What is the third angle? (a) 55° (b) 125° (c) 115° (d) 120°
  4. 4.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°
  5. 5.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 80° (b) 100° (c) 280° (d) 10°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 280° (b) 40° (c) 100° (d) 140°
  7. 7.Two angles of a triangle are 75° and 85°. What is the third angle? (a) 95° (b) 160° (c) 20° (d) 105°
  8. 8.Two angles of a triangle are 45° and 90°. What is the exterior angle at the third corner? (a) 225° (b) 90° (c) 135° (d) 45°
  9. 9.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 120° (c) 145° (d) 35°
  10. 10.Two angles of a triangle are 45° and 35°. What is the third angle? (a) 135° (b) 100° (c) 80° (d) 145°
  11. 11.Two angles of a triangle are 40° and 90°. What is the third angle? (a) 90° (b) 130° (c) 50° (d) 140°
  12. 12.Two angles of a triangle are 20° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 105° (c) 75° (d) 160°
  13. 13.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 140° (c) 40° (d) 50°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 25° (c) 35° (d) 130°
  15. 15.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 145° (b) 215° (c) 36° (d) 35°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 65° (b) 66° (c) 130° (d) 115°
  17. 17.Two angles of a triangle are 30° and 110°. What is the third angle? (a) 140° (b) 150° (c) 70° (d) 40°
  18. 18.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 120° (b) 30° (c) 300° (d) 150°
  19. 19.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) 16° (d) 15°
  20. 20.Two angles of a triangle are 25° and 25°. What is the third angle? (a) 50° (b) 155° (c) 310° (d) 130°
  21. 21.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 150° (c) 135° (d) 30°
  22. 22.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 145° (b) 115° (c) 100° (d) 65°
  23. 23.Two angles of a triangle are 25° and 50°. What is the third angle? (a) 155° (b) 105° (c) 130° (d) 75°
  24. 24.Two angles of a triangle are 25° and 25°. What is the exterior angle at the third corner? (a) 50° (b) 310° (c) 155° (d) 130°
  25. 25.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 121° (b) 120° (c) 60° (d) 240°
  26. 26.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 70° (c) 35° (d) 125°
  27. 27.Two angles of a triangle are 25° and 115°. What is the exterior angle at the third corner? (a) 140° (b) 155° (c) 65° (d) 40°
  28. 28.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 50° (c) 70° (d) 140°
  29. 29.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) 210° (d) 75°
  30. 30.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°
  31. 31.Two angles of a triangle are 70° and 45°. What is the exterior angle at the third corner? (a) 65° (b) 135° (c) 115° (d) 110°
  32. 32.Two angles of a triangle are 50° and 105°. What is the third angle? (a) 25° (b) 155° (c) 130° (d) 75°
  33. 33.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 130° (b) 85° (c) 95° (d) 145°
  34. 34.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 20° (b) 290° (c) 70° (d) 110°
  35. 35.Two angles of a triangle are 45° and 20°. What is the exterior angle at the third corner? (a) 135° (b) 160° (c) 65° (d) 115°
  36. 36.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 80° (c) 40° (d) 50°
  37. 37.Two angles of a triangle are 35° and 55°. What is the third angle? (a) 145° (b) 125° (c) 270° (d) 90°
  38. 38.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°
  39. 39.Two angles of a triangle are 40° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 115° (c) 140° (d) 65°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 51° (b) 130° (c) 50° (d) 100°

Answer key

  1. 85°
  2. 15°
  3. 55°
  4. 30°
  5. 100°
  6. 140°
  7. 20°
  8. 135°
  9. 145°
  10. 100°
  11. 50°
  12. 105°
  13. 100°
  14. 25°
  15. 35°
  16. 65°
  17. 40°
  18. 150°
  19. 15°
  20. 130°
  21. 150°
  22. 65°
  23. 105°
  24. 50°
  25. 120°
  26. 70°
  27. 140°
  28. 70°
  29. 105°
  30. 65°
  31. 115°
  32. 25°
  33. 95°
  34. 110°
  35. 65°
  36. 80°
  37. 90°
  38. 75°
  39. 65°
  40. 50°

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