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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 322 · 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 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)?
  2. 2.The two shorter sides of a right-angled triangle are 36 cm and 15 cm. How long is the longest side (in cm)?
  3. 3.In a right-angled triangle, one of the other two angles is 19°. What is the third angle (in degrees)?
  4. 4.In triangle ABC, angle A = 86° and angle B = 71°. What is angle C (in degrees)?
  5. 5.An exterior angle of a triangle is 131°. One of its two interior opposite angles is 68°. What is the other one (in degrees)?
  6. 6.An exterior angle of a triangle is 85°. One of its two interior opposite angles is 60°. What is the other one (in degrees)?
  7. 7.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)?
  8. 8.The two interior opposite angles of a triangle are 35° and 24°. What is the exterior angle (in degrees)?
  9. 9.The longest side of a right-angled triangle is 26 cm and one of the other sides is 10 cm. How long is the third side (in cm)?
  10. 10.In triangle ABC, angle A = 25° and angle B = 65°. What is angle C (in degrees)?
  11. 11.Can a triangle have sides of 10 cm, 12 cm and 5 cm? (a) No (b) Yes
  12. 12.Can a triangle have sides of 9 cm, 12 cm and 20 cm? (a) No (b) Yes
  13. 13.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)?
  14. 14.The two interior opposite angles of a triangle are 65° and 36°. What is the exterior angle (in degrees)?
  15. 15.Can a triangle have sides of 8 cm, 11 cm and 6 cm? (a) No (b) Yes
  16. 16.The angles of a triangle are in the ratio 2 : 7 : 9. What is the smallest angle (in degrees)?
  17. 17.In triangle ABC, angle A = 24° and angle B = 56°. What is angle C (in degrees)?
  18. 18.In triangle ABC, angle A = 86° and angle B = 29°. What is angle C (in degrees)?
  19. 19.The angles of a triangle are in the ratio 3 : 5 : 7. What is the biggest angle (in degrees)?
  20. 20.The two shorter sides of a right-angled triangle are 7 cm and 24 cm. How long is the longest side (in cm)?
  21. 21.The two interior opposite angles of a triangle are 53° and 74°. What is the exterior angle (in degrees)?
  22. 22.The angles of a triangle are in the ratio 1 : 4 : 5. What is the biggest angle (in degrees)?
  23. 23.An exterior angle of a triangle is 93°. One of its two interior opposite angles is 51°. What is the other one (in degrees)?
  24. 24.An exterior angle of a triangle is 100°. One of its two interior opposite angles is 77°. What is the other one (in degrees)?
  25. 25.Can a triangle have sides of 11 cm, 9 cm and 15 cm? (a) No (b) Yes
  26. 26.Can a triangle have sides of 5 cm, 8 cm and 14 cm? (a) No (b) Yes
  27. 27.An exterior angle of a triangle is 91°. One of its two interior opposite angles is 66°. What is the other one (in degrees)?
  28. 28.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)?
  29. 29.In triangle ABC, angle A = 25° and angle B = 59°. What is angle C (in degrees)?
  30. 30.Can a triangle have sides of 5 cm, 20 cm and 12 cm? (a) Yes (b) No
  31. 31.The two interior opposite angles of a triangle are 52° and 30°. What is the exterior angle (in degrees)?
  32. 32.In a right-angled triangle, one of the other two angles is 54°. What is the third angle (in degrees)?
  33. 33.In triangle ABC, angle A = 21° and angle B = 69°. What is angle C (in degrees)?
  34. 34.In triangle ABC, angle A = 90° and angle B = 56°. What is angle C (in degrees)?
  35. 35.The angles of a triangle are in the ratio 3 : 4 : 5. What is the biggest angle (in degrees)?
  36. 36.In a right-angled triangle, one of the other two angles is 23°. What is the third angle (in degrees)?
  37. 37.The longest side of a right-angled triangle is 13 cm and one of the other sides is 5 cm. How long is the third side (in cm)?
  38. 38.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)?
  39. 39.The two interior opposite angles of a triangle are 72° and 40°. What is the exterior angle (in degrees)?
  40. 40.In a right-angled triangle, one of the other two angles is 60°. What is the third angle (in degrees)?

Answer key

  1. 24
  2. 39
  3. 71
  4. 23
  5. 63
  6. 25
  7. 15
  8. 59
  9. 24
  10. 90
  11. Yes
  12. Yes
  13. 8
  14. 101
  15. Yes
  16. 20
  17. 100
  18. 65
  19. 84
  20. 25
  21. 127
  22. 90
  23. 42
  24. 23
  25. Yes
  26. No
  27. 25
  28. 15
  29. 96
  30. No
  31. 82
  32. 36
  33. 90
  34. 34
  35. 75
  36. 67
  37. 12
  38. 8
  39. 112
  40. 30

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