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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 67 · 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 two equal angles are 25° each. What is the third angle? (a) 25° (b) 130° (c) 65° (d) 155°
  2. 2.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 145° (b) 95° (c) 130° (d) 85°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 70° (c) 35° (d) 110°
  4. 4.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 40° (b) 120° (c) 100° (d) 140°
  5. 5.Two angles of a triangle are 40° and 75°. What is the third angle? (a) 115° (b) 105° (c) 140° (d) 65°
  6. 6.Two angles of a triangle are 55° and 35°. What is the exterior angle at the third corner? (a) 270° (b) 145° (c) 90° (d) 125°
  7. 7.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 30° (b) 100° (c) 150° (d) 110°
  8. 8.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 20° (b) 160° (c) 21° (d) 40°
  9. 9.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 125° (c) 35° (d) 70°
  10. 10.Two angles of a triangle are 40° and 45°. What is the third angle? (a) 140° (b) 95° (c) 135° (d) 85°
  11. 11.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 31° (b) 30° (c) 150° (d) 60°
  12. 12.Two angles of a triangle are 80° and 80°. What is the third angle? (a) 160° (b) 200° (c) 20° (d) 100°
  13. 13.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 55° (b) 70° (c) 20° (d) 110°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 35° (c) 130° (d) 25°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 170° (c) 86° (d) 85°
  16. 16.Two angles of a triangle are 40° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 75° (c) 105° (d) 140°
  17. 17.Two angles of a triangle are 60° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 85° (c) 120° (d) 95°
  18. 18.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 110° (b) 130° (c) 120° (d) 50°
  19. 19.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 105° (b) 110° (c) 145° (d) 75°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 190° (b) 85° (c) 95° (d) 10°
  21. 21.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 60° (b) 110° (c) 120° (d) 130°
  22. 22.Two angles of a triangle are 75° and 30°. What is the third angle? (a) 105° (b) 255° (c) 75° (d) 150°
  23. 23.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 95° (c) 85° (d) 265°
  24. 24.Two angles of a triangle are 25° and 70°. What is the exterior angle at the third corner? (a) 155° (b) 85° (c) 95° (d) 110°
  25. 25.Two angles of a triangle are 60° and 105°. What is the third angle? (a) 75° (b) 120° (c) 15° (d) 165°
  26. 26.Two angles of a triangle are 30° and 140°. What is the third angle? (a) 40° (b) 150° (c) 10° (d) 170°
  27. 27.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 65° (b) 130° (c) 115° (d) 66°
  28. 28.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) 255° (c) 105° (d) 76°
  29. 29.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 110° (c) 40° (d) 70°
  30. 30.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 140° (b) 80° (c) 280° (d) 100°
  31. 31.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 115° (b) 125° (c) 60° (d) 120°
  32. 32.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 120° (b) 130° (c) 110° (d) 70°
  33. 33.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 215° (b) 36° (c) 35° (d) 145°
  34. 34.Two angles of a triangle are 55° and 20°. What is the third angle? (a) 75° (b) 125° (c) 105° (d) 160°
  35. 35.Two angles of a triangle are 20° and 65°. What is the exterior angle at the third corner? (a) 85° (b) 160° (c) 95° (d) 115°
  36. 36.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 50° (c) 40° (d) 140°
  37. 37.Two angles of a triangle are 35° and 100°. What is the exterior angle at the third corner? (a) 145° (b) 80° (c) 45° (d) 135°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 70° (b) 220° (c) 40° (d) 110°
  39. 39.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 100° (c) 10° (d) 50°
  40. 40.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 160° (c) 10° (d) 11°

Answer key

  1. 130°
  2. 95°
  3. 35°
  4. 140°
  5. 65°
  6. 90°
  7. 150°
  8. 20°
  9. 70°
  10. 95°
  11. 30°
  12. 20°
  13. 55°
  14. 25°
  15. 85°
  16. 75°
  17. 85°
  18. 130°
  19. 105°
  20. 95°
  21. 120°
  22. 75°
  23. 85°
  24. 95°
  25. 15°
  26. 10°
  27. 65°
  28. 75°
  29. 40°
  30. 100°
  31. 60°
  32. 70°
  33. 35°
  34. 105°
  35. 85°
  36. 100°
  37. 135°
  38. 110°
  39. 50°
  40. 10°

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