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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 814 · 40 sums
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The method (Inside 180, outside the sum): Angle sum: ∠A + ∠B + ∠C = 180°. Exterior angle = sum of the two interior opposite angles. Right-angled triangle: longest side² = side² + side² (3, 4, 5 and 5, 12, 13 are famous sets). Sides can make a triangle only if the two shorter sides add up to more than the longest side.

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  1. 1.The longest side of a right-angled triangle is 39 cm and one of the other sides is 36 cm. How long is the third side (in cm)?
  2. 2.In triangle ABC, angle A = 58° and angle B = 40°. What is angle C (in degrees)?
  3. 3.Can a triangle have sides of 2 cm, 13 cm and 6 cm? (a) No (b) Yes
  4. 4.The angles of a triangle are in the ratio 1 : 2 : 2. What is the smallest angle (in degrees)?
  5. 5.In an isosceles triangle, the angle between the two equal sides is 38°. What is each of the other two angles (in degrees)?
  6. 6.In triangle ABC, angle A = 70° and angle B = 36°. What is angle C (in degrees)?
  7. 7.In triangle ABC, angle A = 53° and angle B = 73°. What is angle C (in degrees)?
  8. 8.The two shorter sides of a right-angled triangle are 15 cm and 8 cm. How long is the longest side (in cm)?
  9. 9.In an isosceles triangle, the angle between the two equal sides is 22°. What is each of the other two angles (in degrees)?
  10. 10.The angles of a triangle are in the ratio 3 : 3 : 4. What is the smallest angle (in degrees)?
  11. 11.In triangle ABC, angle A = 40° and angle B = 48°. What is angle C (in degrees)?
  12. 12.The angles of a triangle are in the ratio 3 : 5 : 7. What is the smallest angle (in degrees)?
  13. 13.The two shorter sides of a right-angled triangle are 8 cm and 6 cm. How long is the longest side (in cm)?
  14. 14.The angles of a triangle are in the ratio 2 : 3 : 5. What is the smallest angle (in degrees)?
  15. 15.The longest side of a right-angled triangle is 17 cm and one of the other sides is 8 cm. How long is the third side (in cm)?
  16. 16.The longest side of a right-angled triangle is 26 cm and one of the other sides is 10 cm. How long is the third side (in cm)?
  17. 17.An exterior angle of a triangle is 81°. One of its two interior opposite angles is 55°. What is the other one (in degrees)?
  18. 18.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles (in degrees)?
  19. 19.In triangle ABC, angle A = 80° and angle B = 28°. What is angle C (in degrees)?
  20. 20.In triangle ABC, angle A = 45° and angle B = 86°. What is angle C (in degrees)?
  21. 21.The longest side of a right-angled triangle is 25 cm and one of the other sides is 24 cm. How long is the third side (in cm)?
  22. 22.In triangle ABC, angle A = 83° and angle B = 20°. What is angle C (in degrees)?
  23. 23.In a right-angled triangle, one of the other two angles is 21°. What is the third angle (in degrees)?
  24. 24.In a right-angled triangle, one of the other two angles is 59°. What is the third angle (in degrees)?
  25. 25.In triangle ABC, angle A = 79° and angle B = 65°. What is angle C (in degrees)?
  26. 26.The angles of a triangle are in the ratio 1 : 3 : 5. What is the smallest angle (in degrees)?
  27. 27.In a right-angled triangle, one of the other two angles is 34°. What is the third angle (in degrees)?
  28. 28.An exterior angle of a triangle is 111°. One of its two interior opposite angles is 57°. What is the other one (in degrees)?
  29. 29.In a right-angled triangle, one of the other two angles is 63°. What is the third angle (in degrees)?
  30. 30.Can a triangle have sides of 4 cm, 6 cm and 4 cm? (a) No (b) Yes
  31. 31.In a right-angled triangle, one of the other two angles is 58°. What is the third angle (in degrees)?
  32. 32.The angles of a triangle are in the ratio 1 : 1 : 2. What is the biggest angle (in degrees)?
  33. 33.In a right-angled triangle, one of the other two angles is 70°. What is the third angle (in degrees)?
  34. 34.The longest side of a right-angled triangle is 25 cm and one of the other sides is 7 cm. How long is the third side (in cm)?
  35. 35.In an isosceles triangle, the two equal angles are 41° each. What is the third angle (in degrees)?
  36. 36.In triangle ABC, angle A = 62° and angle B = 63°. What is angle C (in degrees)?
  37. 37.An exterior angle of a triangle is 111°. One of its two interior opposite angles is 76°. What is the other one (in degrees)?
  38. 38.In an isosceles triangle, the two equal angles are 67° each. What is the third angle (in degrees)?
  39. 39.Can a triangle have sides of 3 cm, 16 cm and 8 cm? (a) No (b) Yes
  40. 40.Can a triangle have sides of 4 cm, 6 cm and 7 cm? (a) No (b) Yes

Answer key

  1. 15
  2. 82
  3. No
  4. 36
  5. 71
  6. 74
  7. 54
  8. 17
  9. 79
  10. 54
  11. 92
  12. 36
  13. 10
  14. 36
  15. 15
  16. 24
  17. 26
  18. 30
  19. 72
  20. 49
  21. 7
  22. 77
  23. 69
  24. 31
  25. 36
  26. 20
  27. 56
  28. 54
  29. 27
  30. Yes
  31. 32
  32. 90
  33. 20
  34. 24
  35. 98
  36. 55
  37. 35
  38. 46
  39. No
  40. Yes

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