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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 203 · 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.

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  1. 1.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 80° (b) 41° (c) 140° (d) 40°
  2. 2.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 35° (c) 70° (d) 55°
  3. 3.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 61° (b) 240° (c) 120° (d) 60°
  4. 4.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) 76° (d) 105°
  5. 5.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 305° (b) 55° (c) 125° (d) 35°
  6. 6.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 30° (c) 120° (d) 60°
  7. 7.Two angles of a triangle are 35° and 110°. What is the exterior angle at the third corner? (a) 70° (b) 35° (c) 215° (d) 145°
  8. 8.Two angles of a triangle are 50° and 90°. What is the third angle? (a) 90° (b) 140° (c) 40° (d) 130°
  9. 9.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 100° (c) 80° (d) 110°
  10. 10.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 50° (c) 140° (d) 100°
  11. 11.Two angles of a triangle are 20° and 125°. What is the exterior angle at the third corner? (a) 145° (b) 160° (c) 35° (d) 55°
  12. 12.Two angles of a triangle are 55° and 110°. What is the third angle? (a) 165° (b) 125° (c) 70° (d) 15°
  13. 13.Two angles of a triangle are 35° and 75°. What is the exterior angle at the third corner? (a) 145° (b) 105° (c) 110° (d) 70°
  14. 14.Two angles of a triangle are 45° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 135° (c) 55° (d) 125°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 30° (c) 75° (d) 150°
  16. 16.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 85° (c) 95° (d) 10°
  17. 17.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°
  18. 18.Two angles of a triangle are 45° and 115°. What is the third angle? (a) 135° (b) 65° (c) 160° (d) 20°
  19. 19.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 240° (b) 60° (c) 120° (d) 121°
  20. 20.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 40° (b) 320° (c) 50° (d) 140°
  21. 21.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 10° (c) 20° (d) 160°
  22. 22.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 120° (b) 90° (c) 150° (d) 30°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 40° (b) 110° (c) 70° (d) 220°
  24. 24.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 46° (c) 55° (d) 45°
  25. 25.Two angles of a triangle are 55° and 80°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 100° (d) 125°
  26. 26.Two angles of a triangle are 30° and 105°. What is the third angle? (a) 45° (b) 150° (c) 75° (d) 135°
  27. 27.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 80° (b) 260° (c) 50° (d) 130°
  28. 28.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 80° (b) 155° (c) 105° (d) 100°
  29. 29.Two angles of a triangle are 75° and 40°. What is the exterior angle at the third corner? (a) 65° (b) 105° (c) 140° (d) 115°
  30. 30.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 80° (b) 100° (c) 10° (d) 280°
  31. 31.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 115° (b) 65° (c) 66° (d) 245°
  32. 32.Two angles of a triangle are 45° and 125°. What is the third angle? (a) 135° (b) 170° (c) 55° (d) 10°
  33. 33.Two angles of a triangle are 30° and 120°. What is the exterior angle at the third corner? (a) 150° (b) 210° (c) 60° (d) 30°
  34. 34.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 100° (b) 81° (c) 80° (d) 260°
  35. 35.Two angles of a triangle are 20° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 65° (c) 115° (d) 160°
  36. 36.Two angles of a triangle are 65° and 40°. What is the third angle? (a) 105° (b) 140° (c) 115° (d) 75°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 50° (c) 80° (d) 40°
  38. 38.Two angles of a triangle are 25° and 115°. What is the exterior angle at the third corner? (a) 155° (b) 40° (c) 65° (d) 140°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 95° (c) 85° (d) 170°
  40. 40.Two angles of a triangle are 25° and 50°. What is the third angle? (a) 105° (b) 155° (c) 75° (d) 130°

Answer key

  1. 40°
  2. 70°
  3. 60°
  4. 75°
  5. 125°
  6. 120°
  7. 145°
  8. 40°
  9. 100°
  10. 100°
  11. 145°
  12. 15°
  13. 110°
  14. 125°
  15. 75°
  16. 10°
  17. 35°
  18. 20°
  19. 120°
  20. 140°
  21. 10°
  22. 150°
  23. 110°
  24. 45°
  25. 135°
  26. 45°
  27. 130°
  28. 100°
  29. 115°
  30. 100°
  31. 65°
  32. 10°
  33. 150°
  34. 80°
  35. 115°
  36. 75°
  37. 40°
  38. 140°
  39. 85°
  40. 105°

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