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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 559 · 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.In triangle ABC, angle A = 31° and angle B = 118°. What is angle C (in degrees)?
  2. 2.In a right-angled triangle, one of the other two angles is 25°. What is the third angle (in degrees)?
  3. 3.The angles of a triangle are in the ratio 3 : 5 : 7. What is the smallest angle (in degrees)?
  4. 4.An exterior angle of a triangle is 128°. One of its two interior opposite angles is 55°. What is the other one (in degrees)?
  5. 5.In triangle ABC, angle A = 28° and angle B = 117°. What is angle C (in degrees)?
  6. 6.The two shorter sides of a right-angled triangle are 15 cm and 20 cm. How long is the longest side (in cm)?
  7. 7.In an isosceles triangle, the angle between the two equal sides is 152°. What is each of the other two angles (in degrees)?
  8. 8.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)?
  9. 9.In an isosceles triangle, the angle between the two equal sides is 82°. What is each of the other two angles (in degrees)?
  10. 10.In a right-angled triangle, one of the other two angles is 16°. What is the third angle (in degrees)?
  11. 11.In a right-angled triangle, one of the other two angles is 71°. What is the third angle (in degrees)?
  12. 12.The two interior opposite angles of a triangle are 35° and 47°. What is the exterior angle (in degrees)?
  13. 13.In a right-angled triangle, one of the other two angles is 20°. What is the third angle (in degrees)?
  14. 14.In a right-angled triangle, one of the other two angles is 53°. What is the third angle (in degrees)?
  15. 15.An exterior angle of a triangle is 109°. One of its two interior opposite angles is 38°. What is the other one (in degrees)?
  16. 16.The two interior opposite angles of a triangle are 42° and 55°. What is the exterior angle (in degrees)?
  17. 17.In a right-angled triangle, one of the other two angles is 47°. What is the third angle (in degrees)?
  18. 18.The angles of a triangle are in the ratio 3 : 3 : 4. What is the smallest angle (in degrees)?
  19. 19.In an isosceles triangle, the angle between the two equal sides is 104°. What is each of the other two angles (in degrees)?
  20. 20.An exterior angle of a triangle is 158°. One of its two interior opposite angles is 80°. What is the other one (in degrees)?
  21. 21.In triangle ABC, angle A = 25° and angle B = 59°. What is angle C (in degrees)?
  22. 22.In a right-angled triangle, one of the other two angles is 68°. What is the third angle (in degrees)?
  23. 23.Can a triangle have sides of 2 cm, 3 cm and 8 cm? (a) Yes (b) No
  24. 24.The angles of a triangle are in the ratio 2 : 3 : 4. What is the biggest angle (in degrees)?
  25. 25.An exterior angle of a triangle is 86°. One of its two interior opposite angles is 33°. What is the other one (in degrees)?
  26. 26.In triangle ABC, angle A = 21° and angle B = 84°. What is angle C (in degrees)?
  27. 27.The angles of a triangle are in the ratio 1 : 4 : 5. What is the smallest angle (in degrees)?
  28. 28.In triangle ABC, angle A = 59° and angle B = 30°. What is angle C (in degrees)?
  29. 29.In a right-angled triangle, one of the other two angles is 27°. What is the third angle (in degrees)?
  30. 30.In an isosceles triangle, the angle between the two equal sides is 98°. What is each of the other two angles (in degrees)?
  31. 31.In an isosceles triangle, the angle between the two equal sides is 42°. What is each of the other two angles (in degrees)?
  32. 32.In a right-angled triangle, one of the other two angles is 42°. What is the third angle (in degrees)?
  33. 33.The two shorter sides of a right-angled triangle are 3 cm and 4 cm. How long is the longest side (in cm)?
  34. 34.The longest side of a right-angled triangle is 20 cm and one of the other sides is 12 cm. How long is the third side (in cm)?
  35. 35.The angles of a triangle are in the ratio 2 : 3 : 5. What is the biggest angle (in degrees)?
  36. 36.In a right-angled triangle, one of the other two angles is 74°. What is the third angle (in degrees)?
  37. 37.In triangle ABC, angle A = 88° and angle B = 41°. What is angle C (in degrees)?
  38. 38.In a right-angled triangle, one of the other two angles is 58°. What is the third angle (in degrees)?
  39. 39.The two interior opposite angles of a triangle are 37° and 57°. What is the exterior angle (in degrees)?
  40. 40.The angles of a triangle are in the ratio 1 : 2 : 6. What is the smallest angle (in degrees)?

Answer key

  1. 31
  2. 65
  3. 36
  4. 73
  5. 35
  6. 25
  7. 14
  8. 15
  9. 49
  10. 74
  11. 19
  12. 82
  13. 70
  14. 37
  15. 71
  16. 97
  17. 43
  18. 54
  19. 38
  20. 78
  21. 96
  22. 22
  23. No
  24. 80
  25. 53
  26. 75
  27. 18
  28. 91
  29. 63
  30. 41
  31. 69
  32. 48
  33. 5
  34. 16
  35. 90
  36. 16
  37. 51
  38. 32
  39. 94
  40. 20

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