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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 653 · 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 5 cm and one of the other sides is 4 cm. How long is the third side (in cm)?
  2. 2.The two shorter sides of a right-angled triangle are 5 cm and 12 cm. How long is the longest side (in cm)?
  3. 3.The angles of a triangle are in the ratio 3 : 4 : 5. What is the biggest angle (in degrees)?
  4. 4.In a right-angled triangle, one of the other two angles is 66°. What is the third angle (in degrees)?
  5. 5.The angles of a triangle are in the ratio 2 : 3 : 4. What is the biggest angle (in degrees)?
  6. 6.Can a triangle have sides of 10 cm, 12 cm and 4 cm? (a) No (b) Yes
  7. 7.In an isosceles triangle, the two equal angles are 34° each. What is the third angle (in degrees)?
  8. 8.Can a triangle have sides of 12 cm, 5 cm and 5 cm? (a) No (b) Yes
  9. 9.The angles of a triangle are in the ratio 3 : 5 : 7. What is the smallest angle (in degrees)?
  10. 10.An exterior angle of a triangle is 121°. One of its two interior opposite angles is 41°. What is the other one (in degrees)?
  11. 11.In a right-angled triangle, one of the other two angles is 24°. What is the third angle (in degrees)?
  12. 12.An exterior angle of a triangle is 66°. One of its two interior opposite angles is 35°. What is the other one (in degrees)?
  13. 13.In triangle ABC, angle A = 90° and angle B = 29°. 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 15 cm. How long is the third side (in cm)?
  15. 15.In a right-angled triangle, one of the other two angles is 12°. What is the third angle (in degrees)?
  16. 16.The two shorter sides of a right-angled triangle are 4 cm and 3 cm. How long is the longest side (in cm)?
  17. 17.Can a triangle have sides of 10 cm, 12 cm and 2 cm? (a) No (b) Yes
  18. 18.The two shorter sides of a right-angled triangle are 8 cm and 15 cm. How long is the longest side (in cm)?
  19. 19.Can a triangle have sides of 3 cm, 10 cm and 5 cm? (a) Yes (b) No
  20. 20.In a right-angled triangle, one of the other two angles is 73°. What is the third angle (in degrees)?
  21. 21.The longest side of a right-angled triangle is 13 cm and one of the other sides is 12 cm. How long is the third side (in cm)?
  22. 22.In an isosceles triangle, the angle between the two equal sides is 92°. What is each of the other two angles (in degrees)?
  23. 23.The two interior opposite angles of a triangle are 59° and 20°. What is the exterior angle (in degrees)?
  24. 24.The two shorter sides of a right-angled triangle are 12 cm and 5 cm. How long is the longest side (in cm)?
  25. 25.An exterior angle of a triangle is 78°. One of its two interior opposite angles is 31°. What is the other one (in degrees)?
  26. 26.An exterior angle of a triangle is 74°. One of its two interior opposite angles is 38°. What is the other one (in degrees)?
  27. 27.In an isosceles triangle, the angle between the two equal sides is 94°. What is each of the other two angles (in degrees)?
  28. 28.Can a triangle have sides of 12 cm, 20 cm and 8 cm? (a) Yes (b) No
  29. 29.In triangle ABC, angle A = 33° and angle B = 42°. What is angle C (in degrees)?
  30. 30.An exterior angle of a triangle is 114°. One of its two interior opposite angles is 44°. What is the other one (in degrees)?
  31. 31.Can a triangle have sides of 2 cm, 6 cm and 6 cm? (a) Yes (b) No
  32. 32.An exterior angle of a triangle is 92°. One of its two interior opposite angles is 66°. What is the other one (in degrees)?
  33. 33.Can a triangle have sides of 9 cm, 9 cm and 23 cm? (a) Yes (b) No
  34. 34.The angles of a triangle are in the ratio 2 : 7 : 9. What is the smallest angle (in degrees)?
  35. 35.In triangle ABC, angle A = 24° and angle B = 89°. What is angle C (in degrees)?
  36. 36.The angles of a triangle are in the ratio 1 : 4 : 5. What is the biggest angle (in degrees)?
  37. 37.Can a triangle have sides of 6 cm, 13 cm and 6 cm? (a) No (b) Yes
  38. 38.An exterior angle of a triangle is 106°. One of its two interior opposite angles is 62°. What is the other one (in degrees)?
  39. 39.The angles of a triangle are in the ratio 1 : 2 : 3. What is the biggest angle (in degrees)?
  40. 40.In an isosceles triangle, the angle between the two equal sides is 88°. What is each of the other two angles (in degrees)?

Answer key

  1. 3
  2. 13
  3. 75
  4. 24
  5. 80
  6. Yes
  7. 112
  8. No
  9. 36
  10. 80
  11. 66
  12. 31
  13. 61
  14. 20
  15. 78
  16. 5
  17. No
  18. 17
  19. No
  20. 17
  21. 5
  22. 44
  23. 79
  24. 13
  25. 47
  26. 36
  27. 43
  28. No
  29. 105
  30. 70
  31. Yes
  32. 26
  33. No
  34. 20
  35. 67
  36. 90
  37. No
  38. 44
  39. 90
  40. 46

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