← Angles and triangles lesson New set →

Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 516 · 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.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 160° (c) 11° (d) 10°
  2. 2.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 41° (b) 40° (c) 140° (d) 220°
  3. 3.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 85° (b) 155° (c) 120° (d) 95°
  4. 4.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 325° (b) 145° (c) 55° (d) 35°
  5. 5.Two angles of a triangle are 20° and 20°. What is the exterior angle at the third corner? (a) 40° (b) 320° (c) 160° (d) 140°
  6. 6.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) 136° (c) 45° (d) 135°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 40° (c) 80° (d) 50°
  8. 8.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 30° (c) 150° (d) 75°
  9. 9.Two angles of a triangle are 65° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 65° (c) 245° (d) 115°
  10. 10.Two angles of a triangle are 20° and 65°. What is the exterior angle at the third corner? (a) 95° (b) 115° (c) 160° (d) 85°
  11. 11.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 105° (b) 145° (c) 110° (d) 75°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 50° (c) 10° (d) 100°
  13. 13.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 95° (c) 265° (d) 86°
  14. 14.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 145° (d) 120°
  15. 15.Two angles of a triangle are 50° and 120°. What is the third angle? (a) 60° (b) 130° (c) 10° (d) 170°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 30° (c) 25° (d) 15°
  17. 17.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 145° (b) 155° (c) 120° (d) 60°
  18. 18.Two angles of a triangle are 80° and 70°. What is the third angle? (a) 100° (b) 110° (c) 30° (d) 150°
  19. 19.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 105° (b) 76° (c) 255° (d) 75°
  20. 20.Two angles of a triangle are 20° and 150°. What is the third angle? (a) 30° (b) 170° (c) 10° (d) 160°
  21. 21.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 20° (c) 70° (d) 55°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 95° (b) 190° (c) 10° (d) 85°
  23. 23.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 135° (c) 90° (d) 91°
  24. 24.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 15° (b) 165° (c) 105° (d) 90°
  25. 25.Two angles of a triangle are 35° and 65°. What is the exterior angle at the third corner? (a) 145° (b) 115° (c) 100° (d) 80°
  26. 26.Two angles of a triangle are 80° and 55°. What is the third angle? (a) 135° (b) 125° (c) 100° (d) 45°
  27. 27.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 65° (b) 155° (c) 25° (d) 335°
  28. 28.Two angles of a triangle are 75° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 105° (c) 65° (d) 115°
  29. 29.Two angles of a triangle are 55° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 150° (c) 30° (d) 125°
  30. 30.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 95° (b) 85° (c) 160° (d) 105°
  31. 31.Two angles of a triangle are 60° and 50°. What is the third angle? (a) 130° (b) 110° (c) 70° (d) 120°
  32. 32.Two angles of a triangle are 20° and 95°. What is the third angle? (a) 65° (b) 115° (c) 160° (d) 85°
  33. 33.Two angles of a triangle are 25° and 80°. What is the third angle? (a) 105° (b) 155° (c) 75° (d) 100°
  34. 34.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 150° (c) 60° (d) 30°
  35. 35.Two angles of a triangle are 25° and 55°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 125° (d) 155°
  36. 36.Two angles of a triangle are 45° and 25°. What is the third angle? (a) 110° (b) 70° (c) 135° (d) 155°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 145° (b) 35° (c) 290° (d) 110°
  38. 38.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 55° (c) 145° (d) 35°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 86° (c) 85° (d) 95°
  40. 40.Two angles of a triangle are 55° and 45°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 125° (d) 135°

Answer key

  1. 10°
  2. 40°
  3. 95°
  4. 145°
  5. 40°
  6. 135°
  7. 40°
  8. 75°
  9. 115°
  10. 85°
  11. 75°
  12. 50°
  13. 85°
  14. 95°
  15. 10°
  16. 15°
  17. 60°
  18. 30°
  19. 75°
  20. 10°
  21. 55°
  22. 95°
  23. 90°
  24. 15°
  25. 100°
  26. 45°
  27. 155°
  28. 115°
  29. 150°
  30. 85°
  31. 70°
  32. 65°
  33. 75°
  34. 120°
  35. 80°
  36. 110°
  37. 145°
  38. 110°
  39. 85°
  40. 100°

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