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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 774 · 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 65° and 60°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 115° (d) 120°
  2. 2.Two angles of a triangle are 40° and 60°. What is the exterior angle at the third corner? (a) 140° (b) 80° (c) 100° (d) 120°
  3. 3.Two angles of a triangle are 40° and 50°. What is the third angle? (a) 270° (b) 130° (c) 140° (d) 90°
  4. 4.Two angles of a triangle are 20° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 160° (c) 80° (d) 100°
  5. 5.Two angles of a triangle are 20° and 125°. What is the exterior angle at the third corner? (a) 160° (b) 145° (c) 35° (d) 55°
  6. 6.Two angles of a triangle are 60° and 75°. What is the exterior angle at the third corner? (a) 45° (b) 105° (c) 135° (d) 120°
  7. 7.Two angles of a triangle are 75° and 60°. What is the third angle? (a) 45° (b) 120° (c) 105° (d) 135°
  8. 8.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 20° (b) 11° (c) 10° (d) 170°
  9. 9.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 100° (c) 50° (d) 40°
  10. 10.Two angles of a triangle are 20° and 75°. What is the exterior angle at the third corner? (a) 160° (b) 105° (c) 95° (d) 85°
  11. 11.Two angles of a triangle are 40° and 35°. What is the exterior angle at the third corner? (a) 140° (b) 105° (c) 75° (d) 145°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 10° (c) 11° (d) 20°
  13. 13.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) 145° (c) 36° (d) 35°
  14. 14.Two angles of a triangle are 25° and 120°. What is the exterior angle at the third corner? (a) 60° (b) 35° (c) 155° (d) 145°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 35° (c) 25° (d) 50°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 55° (c) 70° (d) 110°
  17. 17.Two angles of a triangle are 60° and 50°. What is the exterior angle at the third corner? (a) 110° (b) 130° (c) 120° (d) 70°
  18. 18.Two angles of a triangle are 75° and 65°. What is the exterior angle at the third corner? (a) 105° (b) 140° (c) 115° (d) 40°
  19. 19.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 290° (b) 35° (c) 110° (d) 145°
  20. 20.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 130° (c) 65° (d) 50°
  21. 21.Two angles of a triangle are 75° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 120° (c) 105° (d) 60°
  22. 22.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 30° (c) 15° (d) 75°
  23. 23.Two angles of a triangle are 65° and 50°. What is the third angle? (a) 115° (b) 65° (c) 245° (d) 130°
  24. 24.Two angles of a triangle are 45° and 50°. What is the third angle? (a) 85° (b) 130° (c) 95° (d) 135°
  25. 25.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 25° (c) 155° (d) 130°
  26. 26.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 90° (b) 15° (c) 105° (d) 165°
  27. 27.Two angles of a triangle are 35° and 60°. What is the third angle? (a) 95° (b) 120° (c) 145° (d) 85°
  28. 28.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 135° (b) 95° (c) 130° (d) 45°
  29. 29.Two angles of a triangle are 45° and 95°. What is the exterior angle at the third corner? (a) 40° (b) 140° (c) 135° (d) 85°
  30. 30.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 105° (b) 75° (c) 120° (d) 135°
  31. 31.Two angles of a triangle are 20° and 80°. What is the exterior angle at the third corner? (a) 160° (b) 260° (c) 80° (d) 100°
  32. 32.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 285° (b) 105° (c) 75° (d) 15°
  33. 33.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 130° (b) 51° (c) 50° (d) 230°
  34. 34.Two angles of a triangle are 20° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 270° (c) 160° (d) 90°
  35. 35.Two angles of a triangle are 55° and 20°. What is the third angle? (a) 160° (b) 75° (c) 125° (d) 105°
  36. 36.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 95° (c) 265° (d) 86°
  37. 37.Two angles of a triangle are 25° and 65°. What is the exterior angle at the third corner? (a) 270° (b) 155° (c) 115° (d) 90°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 220° (b) 70° (c) 40° (d) 110°
  39. 39.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) 10° (c) 170° (d) 190°
  40. 40.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 40° (c) 70° (d) 110°

Answer key

  1. 125°
  2. 100°
  3. 90°
  4. 80°
  5. 145°
  6. 135°
  7. 45°
  8. 10°
  9. 100°
  10. 95°
  11. 75°
  12. 10°
  13. 35°
  14. 145°
  15. 25°
  16. 55°
  17. 110°
  18. 140°
  19. 145°
  20. 65°
  21. 120°
  22. 30°
  23. 65°
  24. 85°
  25. 130°
  26. 15°
  27. 85°
  28. 45°
  29. 140°
  30. 75°
  31. 100°
  32. 105°
  33. 50°
  34. 90°
  35. 105°
  36. 85°
  37. 90°
  38. 110°
  39. 10°
  40. 40°

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