← Angles and triangles lesson New set →

Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 109 · 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 75° and 30°. What is the exterior angle at the third corner? (a) 75° (b) 255° (c) 105° (d) 150°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 100° (c) 10° (d) 80°
  3. 3.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 10° (c) 5° (d) 95°
  4. 4.Two angles of a triangle are 45° and 80°. What is the third angle? (a) 135° (b) 125° (c) 55° (d) 100°
  5. 5.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 145° (b) 35° (c) 325° (d) 55°
  6. 6.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 65° (c) 115° (d) 25°
  7. 7.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 110° (c) 40° (d) 20°
  8. 8.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 65° (c) 155° (d) 25°
  9. 9.Two angles of a triangle are 45° and 110°. What is the third angle? (a) 70° (b) 25° (c) 135° (d) 155°
  10. 10.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 125° (b) 45° (c) 100° (d) 135°
  11. 11.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 45° (c) 110° (d) 35°
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 130° (b) 65° (c) 66° (d) 115°
  13. 13.Two angles of a triangle are 45° and 95°. What is the exterior angle at the third corner? (a) 140° (b) 135° (c) 40° (d) 85°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 50° (b) 115° (c) 230° (d) 65°
  15. 15.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 115° (b) 65° (c) 100° (d) 145°
  16. 16.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) 55° (d) 70°
  17. 17.Two angles of a triangle are 45° and 100°. What is the exterior angle at the third corner? (a) 35° (b) 80° (c) 135° (d) 145°
  18. 18.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 50° (c) 130° (d) 65°
  19. 19.Two angles of a triangle are 20° and 70°. What is the exterior angle at the third corner? (a) 270° (b) 90° (c) 160° (d) 110°
  20. 20.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 66° (b) 115° (c) 65° (d) 245°
  21. 21.Two angles of a triangle are 20° and 75°. What is the third angle? (a) 160° (b) 105° (c) 85° (d) 95°
  22. 22.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 60° (c) 30° (d) 120°
  23. 23.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 40° (b) 115° (c) 140° (d) 105°
  24. 24.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 235° (b) 55° (c) 110° (d) 125°
  25. 25.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 110° (c) 270° (d) 90°
  26. 26.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 155° (b) 160° (c) 135° (d) 45°
  27. 27.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 70° (b) 160° (c) 110° (d) 130°
  28. 28.Two angles of a triangle are 75° and 60°. What is the third angle? (a) 45° (b) 120° (c) 135° (d) 105°
  29. 29.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 30° (c) 60° (d) 120°
  30. 30.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 85° (c) 86° (d) 95°
  31. 31.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 145° (c) 55° (d) 35°
  32. 32.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 115° (b) 155° (c) 90° (d) 270°
  33. 33.Two angles of a triangle are 25° and 120°. What is the third angle? (a) 60° (b) 155° (c) 35° (d) 145°
  34. 34.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 290° (b) 145° (c) 110° (d) 70°
  35. 35.Two angles of a triangle are 55° and 40°. What is the exterior angle at the third corner? (a) 85° (b) 125° (c) 140° (d) 95°
  36. 36.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 15° (c) 30° (d) 105°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 21° (b) 20° (c) 160° (d) 40°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 20° (c) 160° (d) 10°
  39. 39.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 235° (b) 125° (c) 55° (d) 56°
  40. 40.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 105° (b) 30° (c) 210° (d) 150°

Answer key

  1. 105°
  2. 50°
  3. 10°
  4. 55°
  5. 145°
  6. 50°
  7. 40°
  8. 130°
  9. 25°
  10. 45°
  11. 35°
  12. 65°
  13. 140°
  14. 115°
  15. 65°
  16. 55°
  17. 145°
  18. 65°
  19. 90°
  20. 65°
  21. 85°
  22. 60°
  23. 140°
  24. 55°
  25. 90°
  26. 45°
  27. 70°
  28. 45°
  29. 120°
  30. 85°
  31. 110°
  32. 90°
  33. 35°
  34. 110°
  35. 95°
  36. 30°
  37. 20°
  38. 10°
  39. 55°
  40. 30°

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