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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 676 · 40 sums
TalentJR

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 13 cm and one of the other sides is 5 cm. How long is the third side (in cm)?
  2. 2.Can a triangle have sides of 11 cm, 20 cm and 9 cm? (a) No (b) Yes
  3. 3.Can a triangle have sides of 6 cm, 2 cm and 8 cm? (a) No (b) Yes
  4. 4.The angles of a triangle are in the ratio 3 : 4 : 5. What is the smallest angle (in degrees)?
  5. 5.In a right-angled triangle, one of the other two angles is 39°. What is the third angle (in degrees)?
  6. 6.The two interior opposite angles of a triangle are 22° and 46°. What is the exterior angle (in degrees)?
  7. 7.In an isosceles triangle, the angle between the two equal sides is 52°. What is each of the other two angles (in degrees)?
  8. 8.In an isosceles triangle, the angle between the two equal sides is 84°. What is each of the other two angles (in degrees)?
  9. 9.An exterior angle of a triangle is 59°. One of its two interior opposite angles is 32°. What is the other one (in degrees)?
  10. 10.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)?
  11. 11.In a right-angled triangle, one of the other two angles is 11°. What is the third angle (in degrees)?
  12. 12.In triangle ABC, angle A = 69° and angle B = 52°. What is angle C (in degrees)?
  13. 13.In triangle ABC, angle A = 21° and angle B = 29°. What is angle C (in degrees)?
  14. 14.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles (in degrees)?
  15. 15.The angles of a triangle are in the ratio 4 : 5 : 6. What is the smallest angle (in degrees)?
  16. 16.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)?
  17. 17.The angles of a triangle are in the ratio 2 : 3 : 5. What is the biggest angle (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 longest side of a right-angled triangle is 39 cm and one of the other sides is 15 cm. How long is the third side (in cm)?
  20. 20.The angles of a triangle are in the ratio 3 : 4 : 5. What is the biggest angle (in degrees)?
  21. 21.The longest side of a right-angled triangle is 26 cm and one of the other sides is 24 cm. How long is the third side (in cm)?
  22. 22.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)?
  23. 23.The two shorter sides of a right-angled triangle are 8 cm and 15 cm. How long is the longest side (in cm)?
  24. 24.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles (in degrees)?
  25. 25.The two shorter sides of a right-angled triangle are 15 cm and 20 cm. How long is the longest side (in cm)?
  26. 26.An exterior angle of a triangle is 114°. One of its two interior opposite angles is 45°. What is the other one (in degrees)?
  27. 27.The two interior opposite angles of a triangle are 62° and 64°. What is the exterior angle (in degrees)?
  28. 28.In a right-angled triangle, one of the other two angles is 28°. What is the third angle (in degrees)?
  29. 29.The two shorter sides of a right-angled triangle are 7 cm and 24 cm. How long is the longest side (in cm)?
  30. 30.Can a triangle have sides of 4 cm, 2 cm and 7 cm? (a) Yes (b) No
  31. 31.The two interior opposite angles of a triangle are 38° and 23°. What is the exterior angle (in degrees)?
  32. 32.In triangle ABC, angle A = 97° and angle B = 53°. What is angle C (in degrees)?
  33. 33.In an isosceles triangle, the two equal angles are 81° each. What is the third angle (in degrees)?
  34. 34.Can a triangle have sides of 18 cm, 11 cm and 5 cm? (a) Yes (b) No
  35. 35.In triangle ABC, angle A = 81° and angle B = 27°. What is angle C (in degrees)?
  36. 36.In an isosceles triangle, the two equal angles are 54° each. What is the third angle (in degrees)?
  37. 37.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)?
  38. 38.An exterior angle of a triangle is 96°. One of its two interior opposite angles is 25°. What is the other one (in degrees)?
  39. 39.In triangle ABC, angle A = 28° and angle B = 103°. What is angle C (in degrees)?
  40. 40.The angles of a triangle are in the ratio 3 : 3 : 4. What is the smallest angle (in degrees)?

Answer key

  1. 12
  2. No
  3. No
  4. 45
  5. 51
  6. 68
  7. 64
  8. 48
  9. 27
  10. 5
  11. 79
  12. 59
  13. 130
  14. 45
  15. 48
  16. 15
  17. 90
  18. 36
  19. 36
  20. 75
  21. 10
  22. 24
  23. 17
  24. 70
  25. 25
  26. 69
  27. 126
  28. 62
  29. 25
  30. No
  31. 61
  32. 30
  33. 18
  34. No
  35. 72
  36. 72
  37. 15
  38. 71
  39. 49
  40. 54

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