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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 413 · 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 1 : 1 : 2. What is the biggest angle (in degrees)?
  2. 2.The two interior opposite angles of a triangle are 77° and 45°. What is the exterior angle (in degrees)?
  3. 3.The two interior opposite angles of a triangle are 43° and 59°. What is the exterior angle (in degrees)?
  4. 4.An exterior angle of a triangle is 83°. One of its two interior opposite angles is 35°. What is the other one (in degrees)?
  5. 5.The longest side of a right-angled triangle is 10 cm and one of the other sides is 8 cm. How long is the third side (in cm)?
  6. 6.The two shorter sides of a right-angled triangle are 24 cm and 7 cm. How long is the longest side (in cm)?
  7. 7.An exterior angle of a triangle is 57°. One of its two interior opposite angles is 29°. What is the other one (in degrees)?
  8. 8.In triangle ABC, angle A = 93° and angle B = 52°. What is angle C (in degrees)?
  9. 9.In a right-angled triangle, one of the other two angles is 27°. What is the third angle (in degrees)?
  10. 10.The two interior opposite angles of a triangle are 72° and 53°. What is the exterior angle (in degrees)?
  11. 11.The angles of a triangle are in the ratio 4 : 5 : 6. What is the biggest angle (in degrees)?
  12. 12.An exterior angle of a triangle is 113°. One of its two interior opposite angles is 34°. What is the other one (in degrees)?
  13. 13.In an isosceles triangle, the angle between the two equal sides is 88°. What is each of the other two angles (in degrees)?
  14. 14.The two interior opposite angles of a triangle are 45° and 35°. What is the exterior angle (in degrees)?
  15. 15.In a right-angled triangle, one of the other two angles is 28°. What is the third angle (in degrees)?
  16. 16.An exterior angle of a triangle is 48°. One of its two interior opposite angles is 21°. What is the other one (in degrees)?
  17. 17.The two shorter sides of a right-angled triangle are 4 cm and 3 cm. How long is the longest side (in cm)?
  18. 18.The angles of a triangle are in the ratio 1 : 2 : 3. What is the smallest angle (in degrees)?
  19. 19.The two shorter sides of a right-angled triangle are 36 cm and 15 cm. How long is the longest side (in cm)?
  20. 20.In a right-angled triangle, one of the other two angles is 53°. What is the third angle (in degrees)?
  21. 21.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles (in degrees)?
  22. 22.In an isosceles triangle, the angle between the two equal sides is 36°. What is each of the other two angles (in degrees)?
  23. 23.In a right-angled triangle, one of the other two angles is 25°. What is the third angle (in degrees)?
  24. 24.In an isosceles triangle, the angle between the two equal sides is 156°. What is each of the other two angles (in degrees)?
  25. 25.An exterior angle of a triangle is 101°. One of its two interior opposite angles is 52°. What is the other one (in degrees)?
  26. 26.In triangle ABC, angle A = 100° and angle B = 39°. What is angle C (in degrees)?
  27. 27.The angles of a triangle are in the ratio 3 : 3 : 4. What is the biggest angle (in degrees)?
  28. 28.In a right-angled triangle, one of the other two angles is 50°. What is the third angle (in degrees)?
  29. 29.The angles of a triangle are in the ratio 3 : 4 : 5. What is the smallest angle (in degrees)?
  30. 30.In an isosceles triangle, the angle between the two equal sides is 92°. What is each of the other two angles (in degrees)?
  31. 31.The two interior opposite angles of a triangle are 45° and 22°. What is the exterior angle (in degrees)?
  32. 32.In triangle ABC, angle A = 43° and angle B = 22°. What is angle C (in degrees)?
  33. 33.In a right-angled triangle, one of the other two angles is 64°. What is the third angle (in degrees)?
  34. 34.In a right-angled triangle, one of the other two angles is 57°. What is the third angle (in degrees)?
  35. 35.Can a triangle have sides of 10 cm, 8 cm and 18 cm? (a) Yes (b) No
  36. 36.Can a triangle have sides of 3 cm, 11 cm and 13 cm? (a) Yes (b) No
  37. 37.In a right-angled triangle, one of the other two angles is 23°. What is the third angle (in degrees)?
  38. 38.The angles of a triangle are in the ratio 5 : 6 : 7. What is the biggest angle (in degrees)?
  39. 39.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)?
  40. 40.In an isosceles triangle, the two equal angles are 25° each. What is the third angle (in degrees)?

Answer key

  1. 90
  2. 122
  3. 102
  4. 48
  5. 6
  6. 25
  7. 28
  8. 35
  9. 63
  10. 125
  11. 72
  12. 79
  13. 46
  14. 80
  15. 62
  16. 27
  17. 5
  18. 30
  19. 39
  20. 37
  21. 50
  22. 72
  23. 65
  24. 12
  25. 49
  26. 41
  27. 72
  28. 40
  29. 45
  30. 44
  31. 67
  32. 115
  33. 26
  34. 33
  35. No
  36. Yes
  37. 67
  38. 70
  39. 24
  40. 130

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