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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 692 · 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. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 10° (b) 80° (c) 100° (d) 280°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 10° (b) 160° (c) 20° (d) 11°
  3. 3.Two angles of a triangle are 35° and 115°. What is the exterior angle at the third corner? (a) 145° (b) 30° (c) 65° (d) 150°
  4. 4.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 145° (b) 70° (c) 105° (d) 110°
  5. 5.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 100° (b) 135° (c) 80° (d) 145°
  6. 6.Two angles of a triangle are 70° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 40° (c) 140° (d) 220°
  7. 7.Two angles of a triangle are 25° and 45°. What is the third angle? (a) 155° (b) 135° (c) 70° (d) 110°
  8. 8.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 16° (b) 165° (c) 30° (d) 15°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 76° (b) 75° (c) 105° (d) 150°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 50° (b) 25° (c) 155° (d) 26°
  11. 11.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 55° (b) 125° (c) 70° (d) 250°
  12. 12.Two angles of a triangle are 80° and 65°. What is the third angle? (a) 145° (b) 100° (c) 35° (d) 115°
  13. 13.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 70° (c) 140° (d) 40°
  14. 14.Two angles of a triangle are 60° and 70°. What is the third angle? (a) 120° (b) 130° (c) 110° (d) 50°
  15. 15.Two angles of a triangle are 50° and 65°. What is the third angle? (a) 130° (b) 115° (c) 65° (d) 245°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 30° (b) 75° (c) 210° (d) 105°
  17. 17.Two angles of a triangle are 20° and 70°. What is the third angle? (a) 90° (b) 110° (c) 270° (d) 160°
  18. 18.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) 45° (d) 55°
  19. 19.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 135° (c) 45° (d) 91°
  20. 20.Two angles of a triangle are 30° and 120°. What is the exterior angle at the third corner? (a) 150° (b) 60° (c) 30° (d) 210°
  21. 21.Two angles of a triangle are 50° and 90°. What is the exterior angle at the third corner? (a) 40° (b) 130° (c) 90° (d) 140°
  22. 22.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 100° (b) 115° (c) 145° (d) 65°
  23. 23.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°
  24. 24.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 145° (c) 55° (d) 110°
  25. 25.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 50° (b) 115° (c) 230° (d) 65°
  26. 26.Two angles of a triangle are 35° and 125°. What is the third angle? (a) 20° (b) 160° (c) 145° (d) 55°
  27. 27.Two angles of a triangle are 55° and 85°. What is the third angle? (a) 40° (b) 125° (c) 95° (d) 140°
  28. 28.Two angles of a triangle are 30° and 75°. What is the exterior angle at the third corner? (a) 75° (b) 150° (c) 255° (d) 105°
  29. 29.Two angles of a triangle are 45° and 125°. What is the third angle? (a) 55° (b) 135° (c) 10° (d) 170°
  30. 30.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 51° (b) 230° (c) 50° (d) 130°
  31. 31.Two angles of a triangle are 80° and 20°. What is the third angle? (a) 100° (b) 80° (c) 160° (d) 260°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 130° (c) 25° (d) 35°
  33. 33.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 10° (c) 100° (d) 20°
  34. 34.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 30° (c) 15° (d) 25°
  35. 35.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 60° (b) 120° (c) 240° (d) 61°
  36. 36.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°
  37. 37.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 125° (b) 145° (c) 90° (d) 35°
  38. 38.Two angles of a triangle are 70° and 65°. What is the third angle? (a) 135° (b) 110° (c) 45° (d) 115°
  39. 39.Two angles of a triangle are 50° and 35°. What is the third angle? (a) 130° (b) 145° (c) 85° (d) 95°
  40. 40.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 70° (b) 55° (c) 35° (d) 125°

Answer key

  1. 100°
  2. 10°
  3. 150°
  4. 70°
  5. 100°
  6. 140°
  7. 110°
  8. 15°
  9. 75°
  10. 25°
  11. 125°
  12. 35°
  13. 70°
  14. 50°
  15. 65°
  16. 105°
  17. 90°
  18. 45°
  19. 90°
  20. 150°
  21. 140°
  22. 115°
  23. 85°
  24. 110°
  25. 115°
  26. 20°
  27. 40°
  28. 105°
  29. 10°
  30. 50°
  31. 80°
  32. 25°
  33. 20°
  34. 15°
  35. 60°
  36. 75°
  37. 145°
  38. 45°
  39. 95°
  40. 70°

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