← Angles and triangles lesson New set →

Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 19 · 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 90°. What is each of the other two angles? (a) 46° (b) 45° (c) 55° (d) 90°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 50° (c) 80° (d) 100°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 80° (b) 20° (c) 160° (d) 70°
  4. 4.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 60° (c) 61° (d) 30°
  5. 5.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 85° (b) 155° (c) 120° (d) 95°
  6. 6.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 60° (c) 30° (d) 120°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 20° (b) 11° (c) 170° (d) 10°
  8. 8.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 165° (b) 16° (c) 195° (d) 15°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 160° (c) 10° (d) 20°
  10. 10.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 35° (c) 70° (d) 125°
  11. 11.Two angles of a triangle are 20° and 30°. What is the exterior angle at the third corner? (a) 50° (b) 160° (c) 150° (d) 130°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 60° (c) 70° (d) 30°
  13. 13.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 115° (b) 25° (c) 65° (d) 295°
  14. 14.Two angles of a triangle are 60° and 110°. What is the third angle? (a) 70° (b) 120° (c) 170° (d) 10°
  15. 15.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 95° (b) 275° (c) 5° (d) 85°
  16. 16.Two angles of a triangle are 80° and 20°. What is the third angle? (a) 100° (b) 160° (c) 260° (d) 80°
  17. 17.Two angles of a triangle are 25° and 145°. What is the third angle? (a) 170° (b) 155° (c) 35° (d) 10°
  18. 18.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 170° (c) 95° (d) 85°
  19. 19.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 140° (c) 100° (d) 40°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 200° (b) 20° (c) 80° (d) 100°
  21. 21.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 135° (b) 160° (c) 45° (d) 155°
  22. 22.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 155° (d) 145°
  23. 23.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 75° (c) 110° (d) 105°
  24. 24.Two angles of a triangle are 55° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 125° (c) 60° (d) 120°
  25. 25.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 235° (d) 110°
  26. 26.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 50° (c) 130° (d) 80°
  27. 27.Two angles of a triangle are 45° and 20°. What is the third angle? (a) 135° (b) 160° (c) 65° (d) 115°
  28. 28.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 75° (c) 15° (d) 30°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 210° (b) 30° (c) 75° (d) 105°
  30. 30.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 60° (b) 140° (c) 100° (d) 120°
  31. 31.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 145° (b) 85° (c) 95° (d) 130°
  32. 32.Two angles of a triangle are 20° and 100°. What is the exterior angle at the third corner? (a) 60° (b) 160° (c) 80° (d) 120°
  33. 33.Two angles of a triangle are 25° and 65°. What is the exterior angle at the third corner? (a) 90° (b) 155° (c) 270° (d) 115°
  34. 34.Two angles of a triangle are 25° and 125°. What is the third angle? (a) 155° (b) 150° (c) 30° (d) 55°
  35. 35.Two angles of a triangle are 65° and 35°. What is the third angle? (a) 115° (b) 80° (c) 100° (d) 145°
  36. 36.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°
  37. 37.Two angles of a triangle are 20° and 65°. What is the third angle? (a) 160° (b) 85° (c) 95° (d) 115°
  38. 38.Two angles of a triangle are 20° and 55°. What is the third angle? (a) 160° (b) 75° (c) 125° (d) 105°
  39. 39.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 36° (b) 145° (c) 35° (d) 215°
  40. 40.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 30° (c) 150° (d) 15°

Answer key

  1. 45°
  2. 40°
  3. 80°
  4. 60°
  5. 95°
  6. 120°
  7. 10°
  8. 15°
  9. 10°
  10. 70°
  11. 50°
  12. 60°
  13. 115°
  14. 10°
  15. 95°
  16. 80°
  17. 10°
  18. 85°
  19. 100°
  20. 100°
  21. 135°
  22. 60°
  23. 105°
  24. 120°
  25. 125°
  26. 80°
  27. 115°
  28. 30°
  29. 105°
  30. 120°
  31. 95°
  32. 120°
  33. 90°
  34. 30°
  35. 80°
  36. 35°
  37. 95°
  38. 105°
  39. 35°
  40. 15°

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