← Angles and triangles lesson New set →

Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 59 · 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 40°. What is each of the other two angles? (a) 50° (b) 70° (c) 140° (d) 40°
  2. 2.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 95° (c) 10° (d) 5°
  3. 3.Two angles of a triangle are 45° and 115°. What is the third angle? (a) 20° (b) 160° (c) 65° (d) 135°
  4. 4.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 35° (b) 145° (c) 95° (d) 120°
  5. 5.Two angles of a triangle are 30° and 80°. What is the exterior angle at the third corner? (a) 70° (b) 150° (c) 110° (d) 100°
  6. 6.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) 36° (c) 215° (d) 35°
  7. 7.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 30° (b) 105° (c) 75° (d) 15°
  8. 8.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 121° (b) 240° (c) 60° (d) 120°
  9. 9.Two angles of a triangle are 25° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 70° (c) 110° (d) 155°
  10. 10.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 105° (b) 30° (c) 150° (d) 210°
  11. 11.Two angles of a triangle are 65° and 75°. What is the third angle? (a) 115° (b) 140° (c) 40° (d) 105°
  12. 12.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) 130° (d) 80°
  13. 13.Two angles of a triangle are 30° and 120°. What is the exterior angle at the third corner? (a) 210° (b) 150° (c) 60° (d) 30°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 75° (c) 60° (d) 30°
  15. 15.Two angles of a triangle are 75° and 85°. What is the third angle? (a) 95° (b) 105° (c) 160° (d) 20°
  16. 16.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 70° (b) 150° (c) 100° (d) 110°
  17. 17.Two angles of a triangle are 45° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 270° (c) 91° (d) 90°
  18. 18.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 10° (b) 190° (c) 11° (d) 170°
  19. 19.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 160° (b) 100° (c) 80° (d) 81°
  20. 20.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 225° (b) 45° (c) 135° (d) 46°
  21. 21.Two angles of a triangle are 35° and 25°. What is the third angle? (a) 60° (b) 145° (c) 155° (d) 120°
  22. 22.Two angles of a triangle are 25° and 30°. What is the exterior angle at the third corner? (a) 55° (b) 155° (c) 125° (d) 150°
  23. 23.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) 335° (c) 25° (d) 155°
  24. 24.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 50° (b) 310° (c) 40° (d) 130°
  25. 25.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 155° (c) 65° (d) 25°
  26. 26.Two angles of a triangle are 65° and 85°. What is the third angle? (a) 115° (b) 150° (c) 95° (d) 30°
  27. 27.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 110° (b) 90° (c) 270° (d) 160°
  28. 28.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 150° (b) 155° (c) 55° (d) 125°
  29. 29.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 340° (c) 70° (d) 160°
  30. 30.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 95° (b) 130° (c) 135° (d) 45°
  31. 31.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 330° (b) 30° (c) 150° (d) 60°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 20° (c) 140° (d) 40°
  33. 33.Two angles of a triangle are 20° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 85° (c) 160° (d) 95°
  34. 34.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 50° (c) 40° (d) 65°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 90° (c) 45° (d) 46°
  36. 36.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 120° (c) 30° (d) 60°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 130° (b) 50° (c) 100° (d) 51°
  38. 38.Two angles of a triangle are 45° and 125°. What is the third angle? (a) 170° (b) 55° (c) 135° (d) 10°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 76° (b) 105° (c) 75° (d) 150°
  40. 40.Two angles of a triangle are 20° and 90°. What is the third angle? (a) 70° (b) 110° (c) 160° (d) 90°

Answer key

  1. 70°
  2. 10°
  3. 20°
  4. 145°
  5. 110°
  6. 35°
  7. 30°
  8. 120°
  9. 110°
  10. 30°
  11. 40°
  12. 130°
  13. 150°
  14. 75°
  15. 20°
  16. 110°
  17. 90°
  18. 10°
  19. 80°
  20. 45°
  21. 120°
  22. 55°
  23. 155°
  24. 130°
  25. 130°
  26. 30°
  27. 90°
  28. 55°
  29. 160°
  30. 45°
  31. 150°
  32. 20°
  33. 95°
  34. 65°
  35. 45°
  36. 60°
  37. 50°
  38. 10°
  39. 75°
  40. 70°

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