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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 997 · 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 25 cm and one of the other sides is 7 cm. How long is the third side (in cm)?
  2. 2.The two shorter sides of a right-angled triangle are 24 cm and 7 cm. How long is the longest side (in cm)?
  3. 3.In a right-angled triangle, one of the other two angles is 14°. What is the third angle (in degrees)?
  4. 4.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)?
  5. 5.Can a triangle have sides of 22 cm, 11 cm and 8 cm? (a) Yes (b) No
  6. 6.The longest side of a right-angled triangle is 17 cm and one of the other sides is 15 cm. How long is the third side (in cm)?
  7. 7.In an isosceles triangle, the angle between the two equal sides is 62°. What is each of the other two angles (in degrees)?
  8. 8.In triangle ABC, angle A = 29° and angle B = 35°. What is angle C (in degrees)?
  9. 9.In triangle ABC, angle A = 40° and angle B = 64°. What is angle C (in degrees)?
  10. 10.In triangle ABC, angle A = 34° and angle B = 85°. What is angle C (in degrees)?
  11. 11.In triangle ABC, angle A = 27° and angle B = 98°. What is angle C (in degrees)?
  12. 12.The angles of a triangle are in the ratio 1 : 2 : 3. What is the biggest angle (in degrees)?
  13. 13.In triangle ABC, angle A = 98° and angle B = 25°. What is angle C (in degrees)?
  14. 14.The angles of a triangle are in the ratio 1 : 2 : 2. What is the biggest angle (in degrees)?
  15. 15.The two interior opposite angles of a triangle are 45° and 22°. What is the exterior angle (in degrees)?
  16. 16.In an isosceles triangle, the angle between the two equal sides is 116°. What is each of the other two angles (in degrees)?
  17. 17.In triangle ABC, angle A = 76° and angle B = 64°. What is angle C (in degrees)?
  18. 18.Can a triangle have sides of 7 cm, 7 cm and 14 cm? (a) No (b) Yes
  19. 19.Can a triangle have sides of 3 cm, 9 cm and 7 cm? (a) Yes (b) No
  20. 20.The angles of a triangle are in the ratio 5 : 6 : 7. What is the biggest angle (in degrees)?
  21. 21.The longest side of a right-angled triangle is 25 cm and one of the other sides is 15 cm. How long is the third side (in cm)?
  22. 22.In triangle ABC, angle A = 36° and angle B = 34°. What is angle C (in degrees)?
  23. 23.The angles of a triangle are in the ratio 3 : 5 : 7. What is the smallest angle (in degrees)?
  24. 24.Can a triangle have sides of 10 cm, 24 cm and 10 cm? (a) Yes (b) No
  25. 25.An exterior angle of a triangle is 107°. One of its two interior opposite angles is 31°. What is the other one (in degrees)?
  26. 26.The angles of a triangle are in the ratio 3 : 4 : 5. What is the biggest angle (in degrees)?
  27. 27.The angles of a triangle are in the ratio 2 : 3 : 4. What is the smallest angle (in degrees)?
  28. 28.An exterior angle of a triangle is 89°. One of its two interior opposite angles is 39°. What is the other one (in degrees)?
  29. 29.An exterior angle of a triangle is 114°. One of its two interior opposite angles is 45°. What is the other one (in degrees)?
  30. 30.The two shorter sides of a right-angled triangle are 6 cm and 8 cm. How long is the longest side (in cm)?
  31. 31.The angles of a triangle are in the ratio 3 : 3 : 4. What is the smallest angle (in degrees)?
  32. 32.In triangle ABC, angle A = 44° and angle B = 52°. What is angle C (in degrees)?
  33. 33.In an isosceles triangle, the angle between the two equal sides is 144°. What is each of the other two angles (in degrees)?
  34. 34.The two interior opposite angles of a triangle are 68° and 47°. What is the exterior angle (in degrees)?
  35. 35.In a right-angled triangle, one of the other two angles is 70°. What is the third angle (in degrees)?
  36. 36.The angles of a triangle are in the ratio 2 : 3 : 5. What is the biggest angle (in degrees)?
  37. 37.In an isosceles triangle, the angle between the two equal sides is 146°. What is each of the other two angles (in degrees)?
  38. 38.In an isosceles triangle, the two equal angles are 74° each. What is the third angle (in degrees)?
  39. 39.Can a triangle have sides of 11 cm, 9 cm and 3 cm? (a) Yes (b) No
  40. 40.An exterior angle of a triangle is 122°. One of its two interior opposite angles is 51°. What is the other one (in degrees)?

Answer key

  1. 24
  2. 25
  3. 76
  4. 15
  5. No
  6. 8
  7. 59
  8. 116
  9. 76
  10. 61
  11. 55
  12. 90
  13. 57
  14. 72
  15. 67
  16. 32
  17. 40
  18. No
  19. Yes
  20. 70
  21. 20
  22. 110
  23. 36
  24. No
  25. 76
  26. 75
  27. 40
  28. 50
  29. 69
  30. 10
  31. 54
  32. 84
  33. 18
  34. 115
  35. 20
  36. 90
  37. 17
  38. 32
  39. Yes
  40. 71

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