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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 323 · 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 two shorter sides of a right-angled triangle are 24 cm and 7 cm. How long is the longest side (in cm)?
  2. 2.In triangle ABC, angle A = 87° and angle B = 60°. What is angle C (in degrees)?
  3. 3.The angles of a triangle are in the ratio 1 : 2 : 6. What is the biggest angle (in degrees)?
  4. 4.The angles of a triangle are in the ratio 1 : 2 : 3. What is the smallest angle (in degrees)?
  5. 5.Can a triangle have sides of 9 cm, 16 cm and 2 cm? (a) Yes (b) No
  6. 6.An exterior angle of a triangle is 102°. One of its two interior opposite angles is 59°. What is the other one (in degrees)?
  7. 7.In an isosceles triangle, the angle between the two equal sides is 144°. What is each of the other two angles (in degrees)?
  8. 8.The two shorter sides of a right-angled triangle are 5 cm and 12 cm. How long is the longest side (in cm)?
  9. 9.The two interior opposite angles of a triangle are 35° and 31°. What is the exterior angle (in degrees)?
  10. 10.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)?
  11. 11.In an isosceles triangle, the two equal angles are 63° each. What is the third angle (in degrees)?
  12. 12.An exterior angle of a triangle is 95°. One of its two interior opposite angles is 32°. What is the other one (in degrees)?
  13. 13.In triangle ABC, angle A = 39° and angle B = 110°. What is angle C (in degrees)?
  14. 14.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)?
  15. 15.Can a triangle have sides of 20 cm, 8 cm and 11 cm? (a) Yes (b) No
  16. 16.The longest side of a right-angled triangle is 30 cm and one of the other sides is 18 cm. How long is the third side (in cm)?
  17. 17.An exterior angle of a triangle is 54°. One of its two interior opposite angles is 27°. What is the other one (in degrees)?
  18. 18.The angles of a triangle are in the ratio 2 : 3 : 5. What is the smallest angle (in degrees)?
  19. 19.The angles of a triangle are in the ratio 1 : 2 : 2. What is the biggest angle (in degrees)?
  20. 20.In a right-angled triangle, one of the other two angles is 50°. What is the third angle (in degrees)?
  21. 21.Can a triangle have sides of 10 cm, 15 cm and 9 cm? (a) Yes (b) No
  22. 22.An exterior angle of a triangle is 96°. One of its two interior opposite angles is 62°. What is the other one (in degrees)?
  23. 23.The two interior opposite angles of a triangle are 44° and 56°. What is the exterior angle (in degrees)?
  24. 24.Can a triangle have sides of 10 cm, 14 cm and 6 cm? (a) No (b) Yes
  25. 25.In a right-angled triangle, one of the other two angles is 29°. What is the third angle (in degrees)?
  26. 26.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)?
  27. 27.An exterior angle of a triangle is 100°. One of its two interior opposite angles is 68°. What is the other one (in degrees)?
  28. 28.The angles of a triangle are in the ratio 1 : 4 : 5. What is the biggest angle (in degrees)?
  29. 29.Can a triangle have sides of 10 cm, 2 cm and 16 cm? (a) Yes (b) No
  30. 30.In triangle ABC, angle A = 28° and angle B = 80°. What is angle C (in degrees)?
  31. 31.The angles of a triangle are in the ratio 3 : 5 : 7. What is the biggest angle (in degrees)?
  32. 32.An exterior angle of a triangle is 106°. One of its two interior opposite angles is 54°. What is the other one (in degrees)?
  33. 33.In triangle ABC, angle A = 38° and angle B = 50°. What is angle C (in degrees)?
  34. 34.In triangle ABC, angle A = 22° and angle B = 92°. What is angle C (in degrees)?
  35. 35.The angles of a triangle are in the ratio 2 : 7 : 9. What is the smallest angle (in degrees)?
  36. 36.In a right-angled triangle, one of the other two angles is 76°. What is the third angle (in degrees)?
  37. 37.The two interior opposite angles of a triangle are 29° and 38°. What is the exterior angle (in degrees)?
  38. 38.An exterior angle of a triangle is 123°. One of its two interior opposite angles is 52°. What is the other one (in degrees)?
  39. 39.The two shorter sides of a right-angled triangle are 10 cm and 24 cm. How long is the longest side (in cm)?
  40. 40.In triangle ABC, angle A = 22° and angle B = 34°. What is angle C (in degrees)?

Answer key

  1. 25
  2. 33
  3. 120
  4. 30
  5. No
  6. 43
  7. 18
  8. 13
  9. 66
  10. 7
  11. 54
  12. 63
  13. 31
  14. 24
  15. No
  16. 24
  17. 27
  18. 36
  19. 72
  20. 40
  21. Yes
  22. 34
  23. 100
  24. Yes
  25. 61
  26. 8
  27. 32
  28. 90
  29. No
  30. 72
  31. 84
  32. 52
  33. 92
  34. 66
  35. 20
  36. 14
  37. 67
  38. 71
  39. 26
  40. 124

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