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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 189 · 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 60°. What is the third angle? (a) 90° (b) 270° (c) 150° (d) 120°
  2. 2.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 120° (b) 240° (c) 121° (d) 60°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 30° (c) 75° (d) 60°
  4. 4.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 150° (b) 30° (c) 330° (d) 60°
  5. 5.Two angles of a triangle are 30° and 80°. What is the third angle? (a) 110° (b) 100° (c) 70° (d) 150°
  6. 6.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) 85° (d) 5°
  7. 7.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 145° (b) 70° (c) 35° (d) 215°
  8. 8.Two angles of a triangle are 55° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 270° (c) 90° (d) 125°
  9. 9.Two angles of a triangle are 40° and 25°. What is the exterior angle at the third corner? (a) 65° (b) 140° (c) 155° (d) 115°
  10. 10.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 35° (b) 90° (c) 125° (d) 145°
  11. 11.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 315° (b) 45° (c) 135° (d) 136°
  12. 12.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 290° (d) 145°
  13. 13.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 170° (b) 20° (c) 10° (d) 11°
  14. 14.Two angles of a triangle are 20° and 120°. What is the third angle? (a) 140° (b) 60° (c) 40° (d) 160°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 40° (c) 50° (d) 130°
  16. 16.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 130° (c) 155° (d) 25°
  17. 17.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 45° (c) 91° (d) 90°
  18. 18.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 40° (c) 70° (d) 20°
  19. 19.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 310° (b) 155° (c) 130° (d) 25°
  20. 20.Two angles of a triangle are 20° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 125° (c) 55° (d) 160°
  21. 21.Two angles of a triangle are 20° and 20°. What is the exterior angle at the third corner? (a) 140° (b) 320° (c) 160° (d) 40°
  22. 22.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 30° (b) 210° (c) 31° (d) 150°
  23. 23.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 25° (b) 35° (c) 130° (d) 50°
  24. 24.Two angles of a triangle are 35° and 95°. What is the third angle? (a) 145° (b) 130° (c) 85° (d) 50°
  25. 25.Two angles of a triangle are 45° and 20°. What is the third angle? (a) 160° (b) 135° (c) 115° (d) 65°
  26. 26.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 140° (c) 30° (d) 20°
  27. 27.Two angles of a triangle are 65° and 65°. What is the third angle? (a) 130° (b) 115° (c) 50° (d) 230°
  28. 28.Two angles of a triangle are 45° and 35°. What is the third angle? (a) 145° (b) 100° (c) 135° (d) 80°
  29. 29.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 100° (b) 150° (c) 80° (d) 130°
  30. 30.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 120° (c) 60° (d) 30°
  31. 31.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°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 45° (c) 90° (d) 46°
  33. 33.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 30° (b) 90° (c) 150° (d) 120°
  34. 34.Two angles of a triangle are 55° and 115°. What is the third angle? (a) 170° (b) 125° (c) 65° (d) 10°
  35. 35.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 75° (b) 130° (c) 155° (d) 105°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 105° (b) 210° (c) 75° (d) 30°
  37. 37.Two angles of a triangle are 70° and 50°. What is the third angle? (a) 110° (b) 60° (c) 130° (d) 120°
  38. 38.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 50° (c) 40° (d) 100°
  39. 39.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 40° (c) 50° (d) 140°
  40. 40.Two angles of a triangle are 20° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 160° (c) 120° (d) 60°

Answer key

  1. 90°
  2. 120°
  3. 75°
  4. 150°
  5. 70°
  6. 95°
  7. 35°
  8. 90°
  9. 65°
  10. 145°
  11. 135°
  12. 70°
  13. 10°
  14. 40°
  15. 65°
  16. 130°
  17. 90°
  18. 40°
  19. 155°
  20. 55°
  21. 40°
  22. 30°
  23. 25°
  24. 50°
  25. 115°
  26. 20°
  27. 50°
  28. 100°
  29. 100°
  30. 60°
  31. 35°
  32. 45°
  33. 150°
  34. 10°
  35. 75°
  36. 105°
  37. 60°
  38. 100°
  39. 70°
  40. 120°

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