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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 343 · 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.Can a triangle have sides of 12 cm, 23 cm and 8 cm? (a) Yes (b) No
  2. 2.In triangle ABC, angle A = 43° and angle B = 84°. What is angle C (in degrees)?
  3. 3.An exterior angle of a triangle is 57°. One of its two interior opposite angles is 26°. What is the other one (in degrees)?
  4. 4.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)?
  5. 5.The angles of a triangle are in the ratio 1 : 1 : 2. What is the smallest angle (in degrees)?
  6. 6.The angles of a triangle are in the ratio 2 : 3 : 5. What is the smallest angle (in degrees)?
  7. 7.In a right-angled triangle, one of the other two angles is 57°. What is the third angle (in degrees)?
  8. 8.The angles of a triangle are in the ratio 2 : 3 : 5. What is the biggest angle (in degrees)?
  9. 9.In an isosceles triangle, the two equal angles are 52° each. What is the third angle (in degrees)?
  10. 10.The angles of a triangle are in the ratio 3 : 5 : 7. What is the smallest angle (in degrees)?
  11. 11.The two interior opposite angles of a triangle are 79° and 39°. What is the exterior angle (in degrees)?
  12. 12.Can a triangle have sides of 9 cm, 12 cm and 26 cm? (a) No (b) Yes
  13. 13.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)?
  14. 14.In triangle ABC, angle A = 31° and angle B = 34°. What is angle C (in degrees)?
  15. 15.In an isosceles triangle, the angle between the two equal sides is 84°. What is each of the other two angles (in degrees)?
  16. 16.In an isosceles triangle, the angle between the two equal sides is 154°. What is each of the other two angles (in degrees)?
  17. 17.The angles of a triangle are in the ratio 1 : 3 : 5. What is the smallest angle (in degrees)?
  18. 18.In an isosceles triangle, the two equal angles are 28° each. What is the third angle (in degrees)?
  19. 19.In an isosceles triangle, the angle between the two equal sides is 68°. What is each of the other two angles (in degrees)?
  20. 20.An exterior angle of a triangle is 152°. One of its two interior opposite angles is 74°. What is the other one (in degrees)?
  21. 21.An exterior angle of a triangle is 98°. One of its two interior opposite angles is 58°. What is the other one (in degrees)?
  22. 22.An exterior angle of a triangle is 62°. One of its two interior opposite angles is 21°. What is the other one (in degrees)?
  23. 23.Can a triangle have sides of 10 cm, 11 cm and 9 cm? (a) No (b) Yes
  24. 24.The angles of a triangle are in the ratio 1 : 2 : 3. What is the biggest angle (in degrees)?
  25. 25.In triangle ABC, angle A = 77° and angle B = 29°. What is angle C (in degrees)?
  26. 26.The angles of a triangle are in the ratio 5 : 6 : 7. What is the smallest angle (in degrees)?
  27. 27.An exterior angle of a triangle is 75°. One of its two interior opposite angles is 21°. What is the other one (in degrees)?
  28. 28.Can a triangle have sides of 10 cm, 17 cm and 3 cm? (a) Yes (b) No
  29. 29.In triangle ABC, angle A = 30° and angle B = 29°. What is angle C (in degrees)?
  30. 30.In a right-angled triangle, one of the other two angles is 69°. What is the third angle (in degrees)?
  31. 31.In a right-angled triangle, one of the other two angles is 23°. What is the third angle (in degrees)?
  32. 32.The two shorter sides of a right-angled triangle are 24 cm and 7 cm. How long is the longest side (in cm)?
  33. 33.In a right-angled triangle, one of the other two angles is 46°. What is the third angle (in degrees)?
  34. 34.In an isosceles triangle, the angle between the two equal sides is 102°. What is each of the other two angles (in degrees)?
  35. 35.In a right-angled triangle, one of the other two angles is 32°. What is the third angle (in degrees)?
  36. 36.The longest side of a right-angled triangle is 30 cm and one of the other sides is 24 cm. How long is the third side (in cm)?
  37. 37.Can a triangle have sides of 12 cm, 21 cm and 6 cm? (a) Yes (b) No
  38. 38.In triangle ABC, angle A = 37° and angle B = 59°. What is angle C (in degrees)?
  39. 39.The two shorter sides of a right-angled triangle are 8 cm and 15 cm. How long is the longest side (in cm)?
  40. 40.An exterior angle of a triangle is 108°. One of its two interior opposite angles is 69°. What is the other one (in degrees)?

Answer key

  1. No
  2. 53
  3. 31
  4. 36
  5. 45
  6. 36
  7. 33
  8. 90
  9. 76
  10. 36
  11. 118
  12. No
  13. 20
  14. 115
  15. 48
  16. 13
  17. 20
  18. 124
  19. 56
  20. 78
  21. 40
  22. 41
  23. Yes
  24. 90
  25. 74
  26. 50
  27. 54
  28. No
  29. 121
  30. 21
  31. 67
  32. 25
  33. 44
  34. 39
  35. 58
  36. 18
  37. No
  38. 84
  39. 17
  40. 39

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