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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 424 · 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 50° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 230° (c) 130° (d) 50°
  2. 2.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 120° (b) 160° (c) 60° (d) 140°
  3. 3.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 250° (b) 70° (c) 71° (d) 110°
  4. 4.Two angles of a triangle are 50° and 35°. What is the third angle? (a) 85° (b) 95° (c) 130° (d) 145°
  5. 5.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 30° (c) 15° (d) 75°
  6. 6.Two angles of a triangle are 40° and 55°. What is the exterior angle at the third corner? (a) 140° (b) 125° (c) 95° (d) 85°
  7. 7.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 40° (b) 130° (c) 50° (d) 310°
  8. 8.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 75° (b) 110° (c) 105° (d) 145°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 25° (c) 15° (d) 30°
  10. 10.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) 35° (d) 110°
  11. 11.Two angles of a triangle are 25° and 130°. What is the third angle? (a) 25° (b) 155° (c) 205° (d) 50°
  12. 12.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 155° (b) 95° (c) 120° (d) 85°
  13. 13.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 80° (c) 50° (d) 130°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 95° (b) 190° (c) 85° (d) 10°
  15. 15.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 80° (b) 125° (c) 135° (d) 100°
  16. 16.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 105° (b) 15° (c) 285° (d) 75°
  17. 17.Two angles of a triangle are 45° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 135° (c) 115° (d) 65°
  18. 18.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 165° (b) 110° (c) 15° (d) 85°
  19. 19.Two angles of a triangle are 30° and 120°. What is the exterior angle at the third corner? (a) 210° (b) 30° (c) 60° (d) 150°
  20. 20.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 10° (c) 100° (d) 50°
  21. 21.Two angles of a triangle are 65° and 50°. What is the exterior angle at the third corner? (a) 245° (b) 130° (c) 115° (d) 65°
  22. 22.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 65° (c) 130° (d) 40°
  23. 23.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 60° (b) 30° (c) 120° (d) 40°
  24. 24.Two angles of a triangle are 30° and 55°. What is the exterior angle at the third corner? (a) 95° (b) 150° (c) 85° (d) 125°
  25. 25.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 105° (b) 30° (c) 75° (d) 210°
  26. 26.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 35° (c) 125° (d) 70°
  27. 27.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 290° (b) 145° (c) 70° (d) 110°
  28. 28.Two angles of a triangle are 60° and 60°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 121° (d) 240°
  29. 29.Two angles of a triangle are 40° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 120° (c) 140° (d) 60°
  30. 30.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 80° (b) 115° (c) 145° (d) 100°
  31. 31.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 155° (b) 25° (c) 205° (d) 26°
  32. 32.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 45° (b) 130° (c) 95° (d) 135°
  33. 33.Two angles of a triangle are 35° and 100°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 80° (d) 145°
  34. 34.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 160° (c) 340° (d) 70°
  35. 35.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 30° (b) 105° (c) 210° (d) 150°
  36. 36.Two angles of a triangle are 20° and 130°. What is the third angle? (a) 30° (b) 50° (c) 150° (d) 160°
  37. 37.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 275° (b) 85° (c) 5° (d) 95°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 20° (c) 11° (d) 10°
  39. 39.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 61° (c) 30° (d) 120°
  40. 40.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 5° (c) 10° (d) 85°

Answer key

  1. 130°
  2. 60°
  3. 70°
  4. 95°
  5. 30°
  6. 95°
  7. 130°
  8. 105°
  9. 15°
  10. 35°
  11. 25°
  12. 95°
  13. 80°
  14. 95°
  15. 80°
  16. 105°
  17. 65°
  18. 15°
  19. 150°
  20. 50°
  21. 115°
  22. 65°
  23. 30°
  24. 85°
  25. 105°
  26. 70°
  27. 70°
  28. 120°
  29. 60°
  30. 100°
  31. 25°
  32. 45°
  33. 135°
  34. 160°
  35. 30°
  36. 30°
  37. 95°
  38. 10°
  39. 60°
  40. 10°

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