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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 123 · 40 sums
TalentJR

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 two shorter sides of a right-angled triangle are 24 cm and 10 cm. How long is the longest side (in cm)?
  2. 2.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)?
  3. 3.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles (in degrees)?
  4. 4.The two shorter sides of a right-angled triangle are 36 cm and 15 cm. How long is the longest side (in cm)?
  5. 5.An exterior angle of a triangle is 90°. One of its two interior opposite angles is 64°. What is the other one (in degrees)?
  6. 6.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)?
  7. 7.The two interior opposite angles of a triangle are 54° and 56°. What is the exterior angle (in degrees)?
  8. 8.An exterior angle of a triangle is 74°. One of its two interior opposite angles is 43°. What is the other one (in degrees)?
  9. 9.In an isosceles triangle, the two equal angles are 29° each. What is the third angle (in degrees)?
  10. 10.In a right-angled triangle, one of the other two angles is 40°. What is the third angle (in degrees)?
  11. 11.The two shorter sides of a right-angled triangle are 8 cm and 15 cm. How long is the longest side (in cm)?
  12. 12.In triangle ABC, angle A = 58° and angle B = 96°. What is angle C (in degrees)?
  13. 13.In an isosceles triangle, the two equal angles are 56° each. What is the third angle (in degrees)?
  14. 14.The two interior opposite angles of a triangle are 75° and 38°. What is the exterior angle (in degrees)?
  15. 15.The angles of a triangle are in the ratio 2 : 2 : 5. What is the smallest angle (in degrees)?
  16. 16.The two shorter sides of a right-angled triangle are 24 cm and 7 cm. How long is the longest side (in cm)?
  17. 17.In an isosceles triangle, the angle between the two equal sides is 22°. What is each of the other two angles (in degrees)?
  18. 18.Can a triangle have sides of 12 cm, 4 cm and 4 cm? (a) No (b) Yes
  19. 19.In an isosceles triangle, the angle between the two equal sides is 48°. What is each of the other two angles (in degrees)?
  20. 20.In an isosceles triangle, the angle between the two equal sides is 76°. What is each of the other two angles (in degrees)?
  21. 21.An exterior angle of a triangle is 45°. One of its two interior opposite angles is 25°. What is the other one (in degrees)?
  22. 22.An exterior angle of a triangle is 136°. One of its two interior opposite angles is 62°. What is the other one (in degrees)?
  23. 23.An exterior angle of a triangle is 62°. One of its two interior opposite angles is 39°. What is the other one (in degrees)?
  24. 24.In triangle ABC, angle A = 22° and angle B = 35°. What is angle C (in degrees)?
  25. 25.In a right-angled triangle, one of the other two angles is 61°. What is the third angle (in degrees)?
  26. 26.The two shorter sides of a right-angled triangle are 15 cm and 36 cm. How long is the longest side (in cm)?
  27. 27.In an isosceles triangle, the two equal angles are 23° each. What is the third angle (in degrees)?
  28. 28.The angles of a triangle are in the ratio 5 : 6 : 7. What is the biggest angle (in degrees)?
  29. 29.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles (in degrees)?
  30. 30.An exterior angle of a triangle is 124°. One of its two interior opposite angles is 45°. What is the other one (in degrees)?
  31. 31.In a right-angled triangle, one of the other two angles is 56°. What is the third angle (in degrees)?
  32. 32.An exterior angle of a triangle is 58°. One of its two interior opposite angles is 37°. What is the other one (in degrees)?
  33. 33.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)?
  34. 34.In a right-angled triangle, one of the other two angles is 71°. What is the third angle (in degrees)?
  35. 35.The angles of a triangle are in the ratio 3 : 5 : 7. What is the biggest angle (in degrees)?
  36. 36.In a right-angled triangle, one of the other two angles is 55°. What is the third angle (in degrees)?
  37. 37.In a right-angled triangle, one of the other two angles is 13°. What is the third angle (in degrees)?
  38. 38.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles (in degrees)?
  39. 39.The two interior opposite angles of a triangle are 35° and 54°. What is the exterior angle (in degrees)?
  40. 40.The angles of a triangle are in the ratio 3 : 3 : 4. What is the smallest angle (in degrees)?

Answer key

  1. 26
  2. 36
  3. 80
  4. 39
  5. 26
  6. 15
  7. 110
  8. 31
  9. 122
  10. 50
  11. 17
  12. 26
  13. 68
  14. 113
  15. 40
  16. 25
  17. 79
  18. No
  19. 66
  20. 52
  21. 20
  22. 74
  23. 23
  24. 123
  25. 29
  26. 39
  27. 134
  28. 70
  29. 75
  30. 79
  31. 34
  32. 21
  33. 24
  34. 19
  35. 84
  36. 35
  37. 77
  38. 60
  39. 89
  40. 54

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