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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 879 · 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 angles of a triangle are in the ratio 2 : 3 : 4. What is the smallest angle (in degrees)?
  2. 2.In triangle ABC, angle A = 60° and angle B = 76°. What is angle C (in degrees)?
  3. 3.In triangle ABC, angle A = 48° and angle B = 39°. What is angle C (in degrees)?
  4. 4.In an isosceles triangle, the angle between the two equal sides is 72°. What is each of the other two angles (in degrees)?
  5. 5.In triangle ABC, angle A = 87° and angle B = 65°. What is angle C (in degrees)?
  6. 6.In an isosceles triangle, the angle between the two equal sides is 58°. What is each of the other two angles (in degrees)?
  7. 7.The longest side of a right-angled triangle is 39 cm and one of the other sides is 15 cm. How long is the third side (in cm)?
  8. 8.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)?
  9. 9.In an isosceles triangle, the two equal angles are 34° each. What is the third angle (in degrees)?
  10. 10.An exterior angle of a triangle is 106°. One of its two interior opposite angles is 31°. What is the other one (in degrees)?
  11. 11.Can a triangle have sides of 13 cm, 9 cm and 6 cm? (a) Yes (b) No
  12. 12.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles (in degrees)?
  13. 13.Can a triangle have sides of 10 cm, 5 cm and 5 cm? (a) No (b) Yes
  14. 14.An exterior angle of a triangle is 109°. One of its two interior opposite angles is 67°. What is the other one (in degrees)?
  15. 15.In a right-angled triangle, one of the other two angles is 13°. What is the third angle (in degrees)?
  16. 16.In a right-angled triangle, one of the other two angles is 12°. What is the third angle (in degrees)?
  17. 17.In a right-angled triangle, one of the other two angles is 26°. What is the third angle (in degrees)?
  18. 18.The two shorter sides of a right-angled triangle are 12 cm and 9 cm. How long is the longest side (in cm)?
  19. 19.The longest side of a right-angled triangle is 10 cm and one of the other sides is 6 cm. How long is the third side (in cm)?
  20. 20.The angles of a triangle are in the ratio 3 : 5 : 7. What is the biggest angle (in degrees)?
  21. 21.In triangle ABC, angle A = 93° and angle B = 33°. What is angle C (in degrees)?
  22. 22.In a right-angled triangle, one of the other two angles is 25°. What is the third angle (in degrees)?
  23. 23.The two interior opposite angles of a triangle are 26° and 30°. What is the exterior angle (in degrees)?
  24. 24.An exterior angle of a triangle is 133°. One of its two interior opposite angles is 69°. What is the other one (in degrees)?
  25. 25.In triangle ABC, angle A = 21° and angle B = 91°. What is angle C (in degrees)?
  26. 26.The angles of a triangle are in the ratio 2 : 3 : 5. What is the biggest angle (in degrees)?
  27. 27.Can a triangle have sides of 10 cm, 9 cm and 13 cm? (a) No (b) Yes
  28. 28.In triangle ABC, angle A = 37° and angle B = 110°. What is angle C (in degrees)?
  29. 29.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)?
  30. 30.The angles of a triangle are in the ratio 1 : 2 : 6. What is the smallest angle (in degrees)?
  31. 31.In a right-angled triangle, one of the other two angles is 51°. What is the third angle (in degrees)?
  32. 32.The two interior opposite angles of a triangle are 57° and 52°. What is the exterior angle (in degrees)?
  33. 33.In an isosceles triangle, the angle between the two equal sides is 26°. What is each of the other two angles (in degrees)?
  34. 34.In an isosceles triangle, the two equal angles are 64° each. What is the third angle (in degrees)?
  35. 35.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)?
  36. 36.In triangle ABC, angle A = 61° and angle B = 31°. What is angle C (in degrees)?
  37. 37.The two interior opposite angles of a triangle are 77° and 52°. What is the exterior angle (in degrees)?
  38. 38.In triangle ABC, angle A = 36° and angle B = 73°. What is angle C (in degrees)?
  39. 39.In triangle ABC, angle A = 77° and angle B = 21°. What is angle C (in degrees)?
  40. 40.The two interior opposite angles of a triangle are 65° and 21°. What is the exterior angle (in degrees)?

Answer key

  1. 40
  2. 44
  3. 93
  4. 54
  5. 28
  6. 61
  7. 36
  8. 24
  9. 112
  10. 75
  11. Yes
  12. 35
  13. No
  14. 42
  15. 77
  16. 78
  17. 64
  18. 15
  19. 8
  20. 84
  21. 54
  22. 65
  23. 56
  24. 64
  25. 68
  26. 90
  27. Yes
  28. 33
  29. 7
  30. 20
  31. 39
  32. 109
  33. 77
  34. 52
  35. 8
  36. 88
  37. 129
  38. 71
  39. 82
  40. 86

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