← Angles and triangles lesson New set →

Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 323 · 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 20° and 90°. What is the third angle? (a) 90° (b) 160° (c) 70° (d) 110°
  2. 2.Two angles of a triangle are 60° and 90°. What is the third angle? (a) 120° (b) 30° (c) 150° (d) 90°
  3. 3.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 30° (c) 15° (d) 105°
  4. 4.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) 40° (d) 140°
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 165° (b) 16° (c) 30° (d) 15°
  6. 6.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 55° (c) 70° (d) 125°
  7. 7.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 110° (b) 160° (c) 130° (d) 70°
  8. 8.Two angles of a triangle are 30° and 55°. What is the third angle? (a) 125° (b) 95° (c) 150° (d) 85°
  9. 9.Two angles of a triangle are 35° and 90°. What is the third angle? (a) 145° (b) 90° (c) 125° (d) 55°
  10. 10.Two angles of a triangle are 20° and 20°. What is the third angle? (a) 160° (b) 320° (c) 40° (d) 140°
  11. 11.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 85° (b) 160° (c) 105° (d) 95°
  12. 12.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 15° (b) 16° (c) 165° (d) 195°
  13. 13.Two angles of a triangle are 55° and 40°. What is the exterior angle at the third corner? (a) 85° (b) 140° (c) 95° (d) 125°
  14. 14.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 95° (b) 115° (c) 150° (d) 85°
  15. 15.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 20° (b) 200° (c) 160° (d) 21°
  16. 16.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 125° (b) 35° (c) 90° (d) 145°
  17. 17.Two angles of a triangle are 75° and 30°. What is the third angle? (a) 255° (b) 105° (c) 150° (d) 75°
  18. 18.Two angles of a triangle are 20° and 50°. What is the third angle? (a) 110° (b) 160° (c) 130° (d) 70°
  19. 19.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 40° (c) 130° (d) 50°
  20. 20.Two angles of a triangle are 40° and 110°. What is the third angle? (a) 150° (b) 140° (c) 70° (d) 30°
  21. 21.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 250° (b) 55° (c) 125° (d) 70°
  22. 22.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 100° (c) 140° (d) 40°
  23. 23.Two angles of a triangle are 35° and 65°. What is the exterior angle at the third corner? (a) 80° (b) 115° (c) 145° (d) 100°
  24. 24.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 31° (b) 210° (c) 150° (d) 30°
  25. 25.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 125° (b) 115° (c) 120° (d) 60°
  26. 26.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 80° (c) 100° (d) 20°
  27. 27.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°
  28. 28.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 80° (b) 140° (c) 100° (d) 280°
  29. 29.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 60° (c) 120° (d) 160°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 190° (b) 10° (c) 95° (d) 85°
  31. 31.Two angles of a triangle are 25° and 50°. What is the third angle? (a) 155° (b) 75° (c) 105° (d) 130°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 50° (c) 40° (d) 100°
  33. 33.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 40° (c) 65° (d) 130°
  34. 34.Two angles of a triangle are 25° and 25°. What is the third angle? (a) 310° (b) 50° (c) 155° (d) 130°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 90° (b) 270° (c) 45° (d) 135°
  36. 36.Two angles of a triangle are 45° and 95°. What is the third angle? (a) 140° (b) 135° (c) 85° (d) 40°
  37. 37.Two angles of a triangle are 70° and 45°. What is the exterior angle at the third corner? (a) 115° (b) 135° (c) 110° (d) 65°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 290° (b) 145° (c) 110° (d) 35°
  39. 39.Two angles of a triangle are 65° and 30°. What is the exterior angle at the third corner? (a) 115° (b) 150° (c) 85° (d) 95°
  40. 40.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 70° (b) 160° (c) 20° (d) 340°

Answer key

  1. 70°
  2. 30°
  3. 30°
  4. 20°
  5. 15°
  6. 70°
  7. 70°
  8. 95°
  9. 55°
  10. 140°
  11. 85°
  12. 15°
  13. 95°
  14. 85°
  15. 20°
  16. 145°
  17. 75°
  18. 110°
  19. 80°
  20. 30°
  21. 125°
  22. 100°
  23. 100°
  24. 30°
  25. 60°
  26. 20°
  27. 45°
  28. 100°
  29. 60°
  30. 95°
  31. 105°
  32. 40°
  33. 65°
  34. 130°
  35. 135°
  36. 40°
  37. 115°
  38. 145°
  39. 95°
  40. 160°

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