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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 146 · 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 straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 260° (c) 80° (d) 130°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 30° (b) 40° (c) 120° (d) 60°
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 100° (b) 51° (c) 50° (d) 130°
  4. 4.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 110° (c) 70° (d) 35°
  5. 5.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 255° (b) 105° (c) 75° (d) 76°
  6. 6.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 30° (b) 210° (c) 150° (d) 105°
  7. 7.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 75° (c) 105° (d) 30°
  8. 8.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) 230° (c) 51° (d) 50°
  9. 9.Two angles of a triangle are 45° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 145° (c) 135° (d) 35°
  10. 10.Two angles of a triangle are 40° and 105°. What is the exterior angle at the third corner? (a) 35° (b) 75° (c) 140° (d) 145°
  11. 11.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 55° (b) 235° (c) 110° (d) 125°
  12. 12.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 150° (b) 210° (c) 30° (d) 31°
  13. 13.Two angles of a triangle are 55° and 55°. What is the third angle? (a) 125° (b) 250° (c) 70° (d) 110°
  14. 14.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 165° (b) 15° (c) 90° (d) 105°
  15. 15.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 35° (b) 100° (c) 145° (d) 115°
  16. 16.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 100° (c) 80° (d) 105°
  17. 17.Two angles of a triangle are 60° and 75°. What is the exterior angle at the third corner? (a) 45° (b) 105° (c) 120° (d) 135°
  18. 18.Two angles of a triangle are 30° and 100°. What is the third angle? (a) 150° (b) 80° (c) 130° (d) 50°
  19. 19.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 55° (c) 150° (d) 125°
  20. 20.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 20° (b) 80° (c) 10° (d) 100°
  21. 21.Two angles of a triangle are 35° and 125°. What is the third angle? (a) 55° (b) 145° (c) 20° (d) 160°
  22. 22.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 91° (c) 45° (d) 90°
  23. 23.Two angles of a triangle are 45° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 90° (c) 270° (d) 91°
  24. 24.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°
  25. 25.Two angles of a triangle are 65° and 55°. What is the exterior angle at the third corner? (a) 115° (b) 60° (c) 120° (d) 125°
  26. 26.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 55° (b) 56° (c) 125° (d) 235°
  27. 27.Two angles of a triangle are 80° and 50°. What is the third angle? (a) 130° (b) 230° (c) 100° (d) 50°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 95° (b) 10° (c) 190° (d) 85°
  29. 29.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 41° (b) 220° (c) 140° (d) 40°
  30. 30.Two angles of a triangle are 25° and 80°. What is the third angle? (a) 100° (b) 105° (c) 75° (d) 155°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 110° (c) 55° (d) 70°
  32. 32.Two angles of a triangle are 55° and 105°. What is the third angle? (a) 160° (b) 20° (c) 75° (d) 125°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 105° (b) 150° (c) 75° (d) 76°
  34. 34.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 80° (c) 20° (d) 160°
  35. 35.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 80° (b) 155° (c) 25° (d) 125°
  36. 36.Two angles of a triangle are 40° and 35°. What is the exterior angle at the third corner? (a) 105° (b) 145° (c) 140° (d) 75°
  37. 37.Two angles of a triangle are 20° and 30°. What is the third angle? (a) 160° (b) 130° (c) 150° (d) 50°
  38. 38.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 40° (c) 20° (d) 110°
  39. 39.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 35° (b) 95° (c) 145° (d) 120°
  40. 40.Two angles of a triangle are 35° and 60°. What is the exterior angle at the third corner? (a) 145° (b) 85° (c) 120° (d) 95°

Answer key

  1. 130°
  2. 30°
  3. 50°
  4. 35°
  5. 75°
  6. 30°
  7. 30°
  8. 50°
  9. 145°
  10. 145°
  11. 125°
  12. 30°
  13. 70°
  14. 15°
  15. 145°
  16. 100°
  17. 135°
  18. 50°
  19. 55°
  20. 20°
  21. 20°
  22. 90°
  23. 90°
  24. 65°
  25. 120°
  26. 55°
  27. 50°
  28. 95°
  29. 40°
  30. 75°
  31. 55°
  32. 20°
  33. 75°
  34. 80°
  35. 25°
  36. 75°
  37. 130°
  38. 40°
  39. 145°
  40. 95°

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