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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 357 · 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 155°. What is the angle next to it on the same straight line? (a) 26° (b) 155° (c) 205° (d) 25°
  2. 2.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 90° (b) 145° (c) 270° (d) 125°
  3. 3.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 20° (b) 100° (c) 80° (d) 10°
  4. 4.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 155° (b) 45° (c) 135° (d) 70°
  5. 5.Two angles of a triangle are 80° and 50°. What is the exterior angle at the third corner? (a) 230° (b) 100° (c) 50° (d) 130°
  6. 6.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 10° (c) 100° (d) 80°
  7. 7.Two angles of a triangle are 25° and 110°. What is the third angle? (a) 45° (b) 70° (c) 135° (d) 155°
  8. 8.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 66° (b) 115° (c) 245° (d) 65°
  9. 9.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 145° (d) 290°
  10. 10.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 110° (c) 45° (d) 70°
  11. 11.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 145° (b) 85° (c) 95° (d) 130°
  12. 12.Two angles of a triangle are 40° and 95°. What is the third angle? (a) 85° (b) 45° (c) 135° (d) 140°
  13. 13.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 140° (b) 40° (c) 41° (d) 80°
  14. 14.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 110° (b) 80° (c) 150° (d) 100°
  15. 15.Two angles of a triangle are 80° and 70°. What is the third angle? (a) 150° (b) 30° (c) 100° (d) 110°
  16. 16.Two angles of a triangle are 45° and 30°. What is the third angle? (a) 135° (b) 105° (c) 150° (d) 75°
  17. 17.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 90° (c) 46° (d) 45°
  18. 18.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 130° (c) 40° (d) 80°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 80° (c) 20° (d) 70°
  20. 20.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 90° (c) 135° (d) 91°
  21. 21.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 70° (b) 55° (c) 250° (d) 125°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 150° (b) 120° (c) 300° (d) 30°
  23. 23.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 320° (b) 40° (c) 50° (d) 140°
  24. 24.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 130° (c) 155° (d) 25°
  25. 25.Two angles of a triangle are 35° and 85°. What is the exterior angle at the third corner? (a) 145° (b) 60° (c) 95° (d) 120°
  26. 26.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) 30° (d) 150°
  27. 27.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 145° (b) 35° (c) 215° (d) 36°
  28. 28.Two angles of a triangle are 25° and 85°. What is the third angle? (a) 155° (b) 95° (c) 70° (d) 110°
  29. 29.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 10° (c) 5° (d) 95°
  30. 30.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 125° (b) 55° (c) 305° (d) 35°
  31. 31.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 335° (b) 25° (c) 65° (d) 155°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 40° (c) 70° (d) 140°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 160° (b) 140° (c) 320° (d) 20°
  34. 34.Two angles of a triangle are 55° and 55°. What is the third angle? (a) 125° (b) 70° (c) 250° (d) 110°
  35. 35.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 30° (c) 61° (d) 120°
  36. 36.Two angles of a triangle are 45° and 60°. What is the third angle? (a) 75° (b) 105° (c) 120° (d) 135°
  37. 37.Two angles of a triangle are 40° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 140° (c) 75° (d) 105°
  38. 38.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 55° (c) 110° (d) 145°
  39. 39.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 135° (b) 46° (c) 45° (d) 225°
  40. 40.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 260° (b) 81° (c) 80° (d) 100°

Answer key

  1. 25°
  2. 90°
  3. 20°
  4. 135°
  5. 130°
  6. 50°
  7. 45°
  8. 65°
  9. 70°
  10. 35°
  11. 95°
  12. 45°
  13. 40°
  14. 80°
  15. 30°
  16. 105°
  17. 45°
  18. 80°
  19. 80°
  20. 90°
  21. 125°
  22. 150°
  23. 140°
  24. 130°
  25. 120°
  26. 15°
  27. 35°
  28. 70°
  29. 10°
  30. 125°
  31. 155°
  32. 70°
  33. 160°
  34. 70°
  35. 60°
  36. 75°
  37. 105°
  38. 110°
  39. 45°
  40. 80°

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