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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 923 · 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.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 155° (c) 65° (d) 25°
  2. 2.Two angles of a triangle are 45° and 75°. What is the third angle? (a) 60° (b) 135° (c) 120° (d) 105°
  3. 3.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 35° (b) 55° (c) 325° (d) 145°
  4. 4.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 115° (b) 25° (c) 295° (d) 65°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 70° (c) 55° (d) 110°
  6. 6.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 60° (c) 120° (d) 150°
  7. 7.Two angles of a triangle are 30° and 75°. What is the exterior angle at the third corner? (a) 150° (b) 105° (c) 75° (d) 255°
  8. 8.Two angles of a triangle are 55° and 45°. What is the exterior angle at the third corner? (a) 80° (b) 135° (c) 100° (d) 125°
  9. 9.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°
  10. 10.Two angles of a triangle are 50° and 40°. What is the third angle? (a) 90° (b) 270° (c) 140° (d) 130°
  11. 11.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 80° (c) 100° (d) 40°
  12. 12.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 80° (b) 100° (c) 81° (d) 260°
  13. 13.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°
  14. 14.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 110° (c) 70° (d) 40°
  15. 15.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 115° (c) 65° (d) 100°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 150° (c) 60° (d) 30°
  17. 17.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 45° (c) 55° (d) 90°
  18. 18.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 40° (c) 140° (d) 50°
  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) 120° (c) 121° (d) 60°
  20. 20.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 90° (c) 91° (d) 135°
  21. 21.Two angles of a triangle are 20° and 140°. What is the third angle? (a) 40° (b) 200° (c) 160° (d) 20°
  22. 22.Two angles of a triangle are 20° and 130°. What is the third angle? (a) 150° (b) 30° (c) 160° (d) 50°
  23. 23.Two angles of a triangle are 45° and 40°. What is the third angle? (a) 85° (b) 140° (c) 95° (d) 135°
  24. 24.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°
  25. 25.Two angles of a triangle are 60° and 55°. What is the exterior angle at the third corner? (a) 65° (b) 125° (c) 115° (d) 120°
  26. 26.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 70° (b) 250° (c) 55° (d) 125°
  27. 27.Two angles of a triangle are 25° and 60°. What is the exterior angle at the third corner? (a) 95° (b) 120° (c) 85° (d) 155°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 280° (b) 40° (c) 100° (d) 140°
  29. 29.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 25° (b) 105° (c) 155° (d) 100°
  30. 30.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 100° (b) 75° (c) 105° (d) 155°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 60° (b) 70° (c) 120° (d) 30°
  32. 32.Two angles of a triangle are 20° and 45°. What is the exterior angle at the third corner? (a) 65° (b) 135° (c) 115° (d) 160°
  33. 33.Two angles of a triangle are 65° and 90°. What is the third angle? (a) 90° (b) 155° (c) 25° (d) 115°
  34. 34.Two angles of a triangle are 30° and 140°. What is the third angle? (a) 150° (b) 10° (c) 170° (d) 40°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 15° (b) 25° (c) 150° (d) 30°
  36. 36.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 145° (b) 160° (c) 125° (d) 55°
  37. 37.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 5° (c) 95° (d) 10°
  38. 38.Two angles of a triangle are 25° and 80°. What is the third angle? (a) 105° (b) 75° (c) 155° (d) 100°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 160° (b) 320° (c) 140° (d) 20°
  40. 40.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 10° (b) 105° (c) 85° (d) 170°

Answer key

  1. 130°
  2. 60°
  3. 145°
  4. 115°
  5. 55°
  6. 120°
  7. 105°
  8. 100°
  9. 75°
  10. 90°
  11. 40°
  12. 80°
  13. 45°
  14. 40°
  15. 115°
  16. 75°
  17. 45°
  18. 100°
  19. 120°
  20. 90°
  21. 20°
  22. 30°
  23. 95°
  24. 135°
  25. 115°
  26. 125°
  27. 85°
  28. 140°
  29. 25°
  30. 105°
  31. 60°
  32. 65°
  33. 25°
  34. 10°
  35. 15°
  36. 125°
  37. 10°
  38. 75°
  39. 160°
  40. 10°

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