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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 7 · 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 70° and 30°. What is the exterior angle at the third corner? (a) 80° (b) 110° (c) 100° (d) 150°
  2. 2.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°
  3. 3.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 50° (b) 230° (c) 51° (d) 130°
  4. 4.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 75° (b) 135° (c) 105° (d) 150°
  5. 5.Two angles of a triangle are 60° and 50°. What is the third angle? (a) 120° (b) 70° (c) 130° (d) 110°
  6. 6.Two angles of a triangle are 65° and 95°. What is the third angle? (a) 115° (b) 20° (c) 85° (d) 160°
  7. 7.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) 31° (c) 30° (d) 210°
  8. 8.Two angles of a triangle are 35° and 90°. What is the third angle? (a) 90° (b) 145° (c) 55° (d) 125°
  9. 9.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 110° (c) 50° (d) 130°
  10. 10.Two angles of a triangle are 40° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 140° (c) 65° (d) 115°
  11. 11.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 70° (c) 40° (d) 20°
  12. 12.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 315° (b) 45° (c) 136° (d) 135°
  13. 13.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 30° (b) 330° (c) 150° (d) 60°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 135° (b) 46° (c) 45° (d) 90°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 160° (c) 80° (d) 70°
  16. 16.Two angles of a triangle are 55° and 85°. What is the third angle? (a) 140° (b) 95° (c) 40° (d) 125°
  17. 17.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 46° (b) 45° (c) 225° (d) 135°
  18. 18.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 235° (b) 56° (c) 125° (d) 55°
  19. 19.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 165° (b) 30° (c) 15° (d) 16°
  20. 20.Two angles of a triangle are 55° and 35°. What is the exterior angle at the third corner? (a) 125° (b) 145° (c) 270° (d) 90°
  21. 21.Two angles of a triangle are 60° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 110° (c) 120° (d) 70°
  22. 22.Two angles of a triangle are 20° and 20°. What is the third angle? (a) 160° (b) 40° (c) 140° (d) 320°
  23. 23.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 110° (c) 35° (d) 45°
  24. 24.Two angles of a triangle are 30° and 90°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 90° (d) 150°
  25. 25.Two angles of a triangle are 60° and 105°. What is the third angle? (a) 165° (b) 75° (c) 120° (d) 15°
  26. 26.Two angles of a triangle are 20° and 100°. What is the third angle? (a) 160° (b) 80° (c) 120° (d) 60°
  27. 27.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 110° (b) 115° (c) 70° (d) 135°
  28. 28.Two angles of a triangle are 55° and 50°. What is the third angle? (a) 130° (b) 105° (c) 125° (d) 75°
  29. 29.Two angles of a triangle are 55° and 20°. What is the third angle? (a) 160° (b) 125° (c) 75° (d) 105°
  30. 30.Two angles of a triangle are 80° and 85°. What is the third angle? (a) 15° (b) 95° (c) 100° (d) 165°
  31. 31.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 45° (c) 91° (d) 90°
  32. 32.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 55° (c) 145° (d) 110°
  33. 33.Two angles of a triangle are 30° and 55°. What is the third angle? (a) 85° (b) 150° (c) 125° (d) 95°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 100° (b) 20° (c) 80° (d) 200°
  35. 35.Two angles of a triangle are 60° and 55°. What is the third angle? (a) 65° (b) 115° (c) 125° (d) 120°
  36. 36.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 120° (b) 60° (c) 155° (d) 145°
  37. 37.Two angles of a triangle are 75° and 45°. What is the exterior angle at the third corner? (a) 105° (b) 120° (c) 60° (d) 135°
  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) 11° (c) 20° (d) 10°
  39. 39.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 60° (c) 150° (d) 120°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 26° (b) 155° (c) 25° (d) 50°

Answer key

  1. 100°
  2. 10°
  3. 50°
  4. 75°
  5. 70°
  6. 20°
  7. 30°
  8. 55°
  9. 130°
  10. 115°
  11. 40°
  12. 135°
  13. 150°
  14. 45°
  15. 80°
  16. 40°
  17. 45°
  18. 55°
  19. 15°
  20. 90°
  21. 110°
  22. 140°
  23. 35°
  24. 120°
  25. 15°
  26. 60°
  27. 70°
  28. 75°
  29. 105°
  30. 15°
  31. 90°
  32. 110°
  33. 95°
  34. 100°
  35. 65°
  36. 120°
  37. 120°
  38. 10°
  39. 120°
  40. 25°

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