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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 42 · 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 55° and 35°. What is the third angle? (a) 145° (b) 125° (c) 90° (d) 270°
  2. 2.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 155° (d) 160°
  3. 3.Two angles of a triangle are 45° and 50°. What is the exterior angle at the third corner? (a) 95° (b) 135° (c) 130° (d) 85°
  4. 4.Two angles of a triangle are 30° and 55°. What is the exterior angle at the third corner? (a) 85° (b) 150° (c) 95° (d) 125°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 20° (b) 140° (c) 40° (d) 30°
  6. 6.Two angles of a triangle are 65° and 35°. What is the third angle? (a) 145° (b) 80° (c) 100° (d) 115°
  7. 7.Two angles of a triangle are 40° and 110°. What is the exterior angle at the third corner? (a) 70° (b) 140° (c) 150° (d) 30°
  8. 8.Two angles of a triangle are 30° and 65°. What is the third angle? (a) 85° (b) 95° (c) 115° (d) 150°
  9. 9.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 100° (c) 20° (d) 80°
  10. 10.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 130° (c) 25° (d) 65°
  11. 11.Two angles of a triangle are 25° and 120°. What is the third angle? (a) 145° (b) 155° (c) 60° (d) 35°
  12. 12.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 25° (c) 65° (d) 50°
  13. 13.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) 130° (d) 50°
  14. 14.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 55° (b) 125° (c) 110° (d) 235°
  15. 15.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) 56° (d) 55°
  16. 16.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 270° (b) 160° (c) 110° (d) 90°
  17. 17.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 20° (b) 21° (c) 40° (d) 160°
  18. 18.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) 70° (d) 55°
  19. 19.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 75° (b) 155° (c) 130° (d) 105°
  20. 20.Two angles of a triangle are 65° and 40°. What is the third angle? (a) 75° (b) 115° (c) 140° (d) 105°
  21. 21.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 11° (b) 170° (c) 190° (d) 10°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 76° (b) 150° (c) 105° (d) 75°
  23. 23.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 330° (b) 30° (c) 60° (d) 150°
  24. 24.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 170° (b) 10° (c) 140° (d) 50°
  25. 25.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 10° (b) 280° (c) 80° (d) 100°
  26. 26.Two angles of a triangle are 30° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 135° (c) 45° (d) 150°
  27. 27.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 145° (b) 130° (c) 85° (d) 95°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 230° (b) 50° (c) 65° (d) 115°
  29. 29.Two angles of a triangle are 50° and 110°. What is the third angle? (a) 130° (b) 20° (c) 160° (d) 70°
  30. 30.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 120° (b) 155° (c) 145° (d) 60°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 15° (c) 30° (d) 25°
  32. 32.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 110° (c) 40° (d) 20°
  33. 33.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 60° (c) 120° (d) 61°
  34. 34.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 55° (b) 125° (c) 305° (d) 35°
  35. 35.Two angles of a triangle are 30° and 100°. What is the third angle? (a) 50° (b) 150° (c) 80° (d) 130°
  36. 36.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 320° (b) 50° (c) 40° (d) 140°
  37. 37.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°
  38. 38.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 140° (b) 145° (c) 105° (d) 75°
  39. 39.Two angles of a triangle are 55° and 25°. What is the third angle? (a) 155° (b) 100° (c) 80° (d) 125°
  40. 40.Two angles of a triangle are 65° and 85°. What is the third angle? (a) 115° (b) 95° (c) 30° (d) 150°

Answer key

  1. 90°
  2. 45°
  3. 95°
  4. 85°
  5. 20°
  6. 80°
  7. 150°
  8. 85°
  9. 20°
  10. 130°
  11. 35°
  12. 50°
  13. 65°
  14. 55°
  15. 55°
  16. 90°
  17. 20°
  18. 55°
  19. 75°
  20. 75°
  21. 10°
  22. 75°
  23. 150°
  24. 10°
  25. 100°
  26. 135°
  27. 95°
  28. 115°
  29. 20°
  30. 60°
  31. 15°
  32. 40°
  33. 60°
  34. 125°
  35. 50°
  36. 140°
  37. 155°
  38. 105°
  39. 100°
  40. 30°

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