← Angles and triangles lesson New set →

Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 818 · 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 30° and 130°. What is the third angle? (a) 20° (b) 150° (c) 50° (d) 160°
  2. 2.Two angles of a triangle are 70° and 85°. What is the third angle? (a) 155° (b) 95° (c) 110° (d) 25°
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 61° (b) 59° (c) 120° (d) 60°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 75° (b) 210° (c) 105° (d) 30°
  5. 5.Two angles of a triangle are 70° and 50°. What is the third angle? (a) 120° (b) 130° (c) 60° (d) 110°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 55° (b) 70° (c) 125° (d) 250°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 45° (b) 270° (c) 135° (d) 90°
  8. 8.Two angles of a triangle are 35° and 60°. What is the third angle? (a) 120° (b) 85° (c) 145° (d) 95°
  9. 9.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 110° (b) 60° (c) 120° (d) 130°
  10. 10.Two angles of a triangle are 65° and 40°. What is the third angle? (a) 140° (b) 105° (c) 115° (d) 75°
  11. 11.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 130° (b) 135° (c) 45° (d) 95°
  12. 12.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 51° (b) 50° (c) 130° (d) 230°
  13. 13.Two angles of a triangle are 55° and 55°. What is the third angle? (a) 125° (b) 70° (c) 110° (d) 250°
  14. 14.Two angles of a triangle are 20° and 125°. What is the third angle? (a) 145° (b) 55° (c) 160° (d) 35°
  15. 15.Two angles of a triangle are 20° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 95° (c) 160° (d) 85°
  16. 16.Two angles of a triangle are 35° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 115° (c) 65° (d) 145°
  17. 17.Two angles of a triangle are 20° and 85°. What is the third angle? (a) 75° (b) 105° (c) 160° (d) 95°
  18. 18.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 65° (c) 115° (d) 25°
  19. 19.Two angles of a triangle are 40° and 75°. What is the third angle? (a) 140° (b) 115° (c) 105° (d) 65°
  20. 20.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 60° (c) 150° (d) 30°
  21. 21.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 110° (b) 70° (c) 135° (d) 115°
  22. 22.Two angles of a triangle are 55° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 80° (c) 100° (d) 125°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 155° (b) 25° (c) 50° (d) 26°
  24. 24.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 65° (c) 40° (d) 50°
  25. 25.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 145° (b) 160° (c) 125° (d) 55°
  26. 26.Two angles of a triangle are 60° and 110°. What is the third angle? (a) 170° (b) 10° (c) 70° (d) 120°
  27. 27.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 16° (b) 165° (c) 30° (d) 15°
  28. 28.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°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 56° (b) 125° (c) 110° (d) 55°
  30. 30.Two angles of a triangle are 75° and 45°. What is the exterior angle at the third corner? (a) 105° (b) 135° (c) 60° (d) 120°
  31. 31.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 5° (c) 95° (d) 10°
  32. 32.Two angles of a triangle are 80° and 90°. What is the third angle? (a) 90° (b) 170° (c) 10° (d) 100°
  33. 33.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 20° (c) 40° (d) 70°
  34. 34.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 70° (b) 120° (c) 130° (d) 110°
  35. 35.Two angles of a triangle are 50° and 25°. What is the third angle? (a) 130° (b) 75° (c) 105° (d) 155°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 145° (b) 70° (c) 35° (d) 36°
  37. 37.Two angles of a triangle are 80° and 60°. What is the third angle? (a) 140° (b) 120° (c) 100° (d) 40°
  38. 38.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 35° (c) 110° (d) 145°
  39. 39.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 60° (c) 120° (d) 30°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 50° (b) 100° (c) 51° (d) 130°

Answer key

  1. 20°
  2. 25°
  3. 60°
  4. 105°
  5. 60°
  6. 125°
  7. 135°
  8. 85°
  9. 120°
  10. 75°
  11. 45°
  12. 50°
  13. 70°
  14. 35°
  15. 95°
  16. 65°
  17. 75°
  18. 50°
  19. 65°
  20. 75°
  21. 70°
  22. 80°
  23. 25°
  24. 65°
  25. 55°
  26. 10°
  27. 15°
  28. 130°
  29. 55°
  30. 120°
  31. 10°
  32. 10°
  33. 40°
  34. 110°
  35. 105°
  36. 35°
  37. 40°
  38. 110°
  39. 120°
  40. 50°

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