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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 316 · 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 17 cm and one of the other sides is 8 cm. How long is the third side (in cm)?
  2. 2.Can a triangle have sides of 9 cm, 2 cm and 5 cm? (a) No (b) Yes
  3. 3.Can a triangle have sides of 11 cm, 9 cm and 11 cm? (a) No (b) Yes
  4. 4.In an isosceles triangle, the two equal angles are 83° each. What is the third angle (in degrees)?
  5. 5.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)?
  6. 6.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)?
  7. 7.In a right-angled triangle, one of the other two angles is 38°. What is the third angle (in degrees)?
  8. 8.In triangle ABC, angle A = 30° and angle B = 116°. What is angle C (in degrees)?
  9. 9.An exterior angle of a triangle is 105°. One of its two interior opposite angles is 79°. What is the other one (in degrees)?
  10. 10.In triangle ABC, angle A = 71° and angle B = 36°. What is angle C (in degrees)?
  11. 11.In an isosceles triangle, the two equal angles are 74° each. What is the third angle (in degrees)?
  12. 12.In an isosceles triangle, the two equal angles are 57° each. What is the third angle (in degrees)?
  13. 13.The two interior opposite angles of a triangle are 35° and 74°. What is the exterior angle (in degrees)?
  14. 14.The angles of a triangle are in the ratio 2 : 3 : 4. What is the biggest angle (in degrees)?
  15. 15.In a right-angled triangle, one of the other two angles is 61°. What is the third angle (in degrees)?
  16. 16.Can a triangle have sides of 7 cm, 9 cm and 9 cm? (a) Yes (b) No
  17. 17.In an isosceles triangle, the angle between the two equal sides is 96°. What is each of the other two angles (in degrees)?
  18. 18.In triangle ABC, angle A = 100° and angle B = 49°. What is angle C (in degrees)?
  19. 19.An exterior angle of a triangle is 125°. One of its two interior opposite angles is 54°. What is the other one (in degrees)?
  20. 20.In triangle ABC, angle A = 81° and angle B = 70°. What is angle C (in degrees)?
  21. 21.The two shorter sides of a right-angled triangle are 15 cm and 8 cm. How long is the longest side (in cm)?
  22. 22.The angles of a triangle are in the ratio 3 : 4 : 5. What is the smallest angle (in degrees)?
  23. 23.In an isosceles triangle, the angle between the two equal sides is 78°. What is each of the other two angles (in degrees)?
  24. 24.In a right-angled triangle, one of the other two angles is 37°. What is the third angle (in degrees)?
  25. 25.Can a triangle have sides of 19 cm, 10 cm and 5 cm? (a) Yes (b) No
  26. 26.In triangle ABC, angle A = 60° and angle B = 28°. What is angle C (in degrees)?
  27. 27.An exterior angle of a triangle is 105°. One of its two interior opposite angles is 37°. What is the other one (in degrees)?
  28. 28.In triangle ABC, angle A = 49° and angle B = 44°. What is angle C (in degrees)?
  29. 29.The two shorter sides of a right-angled triangle are 10 cm and 24 cm. How long is the longest side (in cm)?
  30. 30.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles (in degrees)?
  31. 31.The angles of a triangle are in the ratio 1 : 2 : 3. What is the smallest angle (in degrees)?
  32. 32.The angles of a triangle are in the ratio 2 : 2 : 5. What is the biggest angle (in degrees)?
  33. 33.In an isosceles triangle, the angle between the two equal sides is 22°. What is each of the other two angles (in degrees)?
  34. 34.In a right-angled triangle, one of the other two angles is 13°. What is the third angle (in degrees)?
  35. 35.An exterior angle of a triangle is 147°. One of its two interior opposite angles is 74°. What is the other one (in degrees)?
  36. 36.In triangle ABC, angle A = 40° and angle B = 99°. What is angle C (in degrees)?
  37. 37.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)?
  38. 38.In triangle ABC, angle A = 41° and angle B = 39°. What is angle C (in degrees)?
  39. 39.Can a triangle have sides of 12 cm, 6 cm and 7 cm? (a) Yes (b) No
  40. 40.Can a triangle have sides of 14 cm, 4 cm and 9 cm? (a) No (b) Yes

Answer key

  1. 15
  2. No
  3. Yes
  4. 14
  5. 24
  6. 15
  7. 52
  8. 34
  9. 26
  10. 73
  11. 32
  12. 66
  13. 109
  14. 80
  15. 29
  16. Yes
  17. 42
  18. 31
  19. 71
  20. 29
  21. 17
  22. 45
  23. 51
  24. 53
  25. No
  26. 92
  27. 68
  28. 87
  29. 26
  30. 15
  31. 30
  32. 100
  33. 79
  34. 77
  35. 73
  36. 41
  37. 7
  38. 100
  39. Yes
  40. No

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