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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 596 · 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 20°. What is the exterior angle at the third corner? (a) 130° (b) 150° (c) 160° (d) 50°
  2. 2.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 75° (b) 76° (c) 105° (d) 255°
  3. 3.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 75° (c) 30° (d) 15°
  4. 4.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 130° (c) 65° (d) 25°
  5. 5.Two angles of a triangle are 30° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 120° (c) 150° (d) 60°
  6. 6.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 70° (b) 130° (c) 110° (d) 160°
  7. 7.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 295° (b) 65° (c) 115° (d) 25°
  8. 8.Two angles of a triangle are 45° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 135° (c) 105° (d) 75°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 270° (b) 135° (c) 45° (d) 90°
  10. 10.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 10° (b) 20° (c) 11° (d) 160°
  11. 11.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 60° (b) 40° (c) 30° (d) 120°
  12. 12.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 115° (c) 80° (d) 100°
  13. 13.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 76° (b) 75° (c) 105° (d) 150°
  14. 14.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 290° (b) 70° (c) 110° (d) 145°
  15. 15.Two angles of a triangle are 30° and 65°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 150° (d) 115°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 20° (b) 40° (c) 140° (d) 30°
  17. 17.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 115° (b) 150° (c) 30° (d) 95°
  18. 18.Two angles of a triangle are 30° and 60°. What is the exterior angle at the third corner? (a) 150° (b) 90° (c) 270° (d) 120°
  19. 19.Two angles of a triangle are 30° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 95° (c) 85° (d) 150°
  20. 20.Two angles of a triangle are 20° and 55°. What is the third angle? (a) 75° (b) 125° (c) 160° (d) 105°
  21. 21.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 40° (b) 105° (c) 140° (d) 115°
  22. 22.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 110° (b) 80° (c) 150° (d) 100°
  23. 23.Two angles of a triangle are 35° and 80°. What is the exterior angle at the third corner? (a) 145° (b) 65° (c) 115° (d) 100°
  24. 24.Two angles of a triangle are 30° and 50°. What is the exterior angle at the third corner? (a) 100° (b) 150° (c) 130° (d) 80°
  25. 25.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 110° (b) 125° (c) 55° (d) 56°
  26. 26.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 140° (b) 75° (c) 145° (d) 105°
  27. 27.Two angles of a triangle are 55° and 20°. What is the third angle? (a) 125° (b) 160° (c) 105° (d) 75°
  28. 28.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°
  29. 29.Two angles of a triangle are 45° and 100°. What is the third angle? (a) 135° (b) 145° (c) 35° (d) 80°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 230° (b) 115° (c) 50° (d) 65°
  31. 31.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) 50° (d) 40°
  32. 32.Two angles of a triangle are 65° and 40°. What is the third angle? (a) 75° (b) 140° (c) 115° (d) 105°
  33. 33.Two angles of a triangle are 35° and 30°. What is the third angle? (a) 150° (b) 65° (c) 115° (d) 145°
  34. 34.Two angles of a triangle are 35° and 30°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 145° (d) 150°
  35. 35.Two angles of a triangle are 40° and 45°. What is the third angle? (a) 95° (b) 85° (c) 140° (d) 135°
  36. 36.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) 136° (d) 135°
  37. 37.Two angles of a triangle are 30° and 60°. What is the third angle? (a) 270° (b) 90° (c) 150° (d) 120°
  38. 38.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 130° (b) 50° (c) 310° (d) 40°
  39. 39.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 75° (c) 105° (d) 155°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 25° (b) 130° (c) 155° (d) 310°

Answer key

  1. 50°
  2. 75°
  3. 30°
  4. 130°
  5. 120°
  6. 70°
  7. 115°
  8. 105°
  9. 135°
  10. 10°
  11. 30°
  12. 100°
  13. 75°
  14. 70°
  15. 95°
  16. 20°
  17. 150°
  18. 90°
  19. 85°
  20. 105°
  21. 40°
  22. 100°
  23. 115°
  24. 80°
  25. 55°
  26. 105°
  27. 105°
  28. 150°
  29. 35°
  30. 115°
  31. 65°
  32. 75°
  33. 115°
  34. 65°
  35. 95°
  36. 135°
  37. 90°
  38. 130°
  39. 75°
  40. 155°

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