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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 100 · 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 17 cm and one of the other sides is 8 cm. How long is the third side (in cm)?
  2. 2.An exterior angle of a triangle is 102°. One of its two interior opposite angles is 46°. What is the other one (in degrees)?
  3. 3.Can a triangle have sides of 19 cm, 10 cm and 10 cm? (a) Yes (b) No
  4. 4.Can a triangle have sides of 8 cm, 9 cm and 3 cm? (a) No (b) Yes
  5. 5.An exterior angle of a triangle is 63°. One of its two interior opposite angles is 28°. What is the other one (in degrees)?
  6. 6.The angles of a triangle are in the ratio 3 : 5 : 7. What is the biggest angle (in degrees)?
  7. 7.In triangle ABC, angle A = 45° and angle B = 68°. What is angle C (in degrees)?
  8. 8.In triangle ABC, angle A = 97° and angle B = 29°. What is angle C (in degrees)?
  9. 9.An exterior angle of a triangle is 95°. One of its two interior opposite angles is 30°. What is the other one (in degrees)?
  10. 10.In triangle ABC, angle A = 50° and angle B = 93°. What is angle C (in degrees)?
  11. 11.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)?
  12. 12.Can a triangle have sides of 15 cm, 7 cm and 7 cm? (a) Yes (b) No
  13. 13.In an isosceles triangle, the angle between the two equal sides is 52°. What is each of the other two angles (in degrees)?
  14. 14.The two shorter sides of a right-angled triangle are 8 cm and 15 cm. How long is the longest side (in cm)?
  15. 15.An exterior angle of a triangle is 105°. One of its two interior opposite angles is 32°. What is the other one (in degrees)?
  16. 16.The angles of a triangle are in the ratio 1 : 2 : 6. What is the smallest angle (in degrees)?
  17. 17.The angles of a triangle are in the ratio 1 : 2 : 3. What is the smallest angle (in degrees)?
  18. 18.Can a triangle have sides of 6 cm, 5 cm and 13 cm? (a) No (b) Yes
  19. 19.In a right-angled triangle, one of the other two angles is 39°. What is the third angle (in degrees)?
  20. 20.Can a triangle have sides of 7 cm, 2 cm and 8 cm? (a) No (b) Yes
  21. 21.In triangle ABC, angle A = 35° and angle B = 49°. What is angle C (in degrees)?
  22. 22.In triangle ABC, angle A = 90° and angle B = 65°. What is angle C (in degrees)?
  23. 23.Can a triangle have sides of 10 cm, 2 cm and 11 cm? (a) No (b) Yes
  24. 24.The longest side of a right-angled triangle is 15 cm and one of the other sides is 12 cm. How long is the third side (in cm)?
  25. 25.In an isosceles triangle, the two equal angles are 60° each. What is the third angle (in degrees)?
  26. 26.In an isosceles triangle, the angle between the two equal sides is 74°. What is each of the other two angles (in degrees)?
  27. 27.The two interior opposite angles of a triangle are 33° and 72°. What is the exterior angle (in degrees)?
  28. 28.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)?
  29. 29.An exterior angle of a triangle is 74°. One of its two interior opposite angles is 34°. What is the other one (in degrees)?
  30. 30.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles (in degrees)?
  31. 31.Can a triangle have sides of 2 cm, 10 cm and 6 cm? (a) Yes (b) No
  32. 32.In an isosceles triangle, the two equal angles are 62° each. What is the third angle (in degrees)?
  33. 33.The two interior opposite angles of a triangle are 74° and 66°. What is the exterior angle (in degrees)?
  34. 34.An exterior angle of a triangle is 79°. One of its two interior opposite angles is 46°. What is the other one (in degrees)?
  35. 35.In an isosceles triangle, the two equal angles are 22° each. What is the third angle (in degrees)?
  36. 36.An exterior angle of a triangle is 98°. One of its two interior opposite angles is 28°. What is the other one (in degrees)?
  37. 37.The angles of a triangle are in the ratio 2 : 3 : 5. What is the biggest angle (in degrees)?
  38. 38.Can a triangle have sides of 10 cm, 5 cm and 5 cm? (a) Yes (b) No
  39. 39.In an isosceles triangle, the two equal angles are 76° each. What is the third angle (in degrees)?
  40. 40.In a right-angled triangle, one of the other two angles is 43°. What is the third angle (in degrees)?

Answer key

  1. 15
  2. 56
  3. Yes
  4. Yes
  5. 35
  6. 84
  7. 67
  8. 54
  9. 65
  10. 37
  11. 12
  12. No
  13. 64
  14. 17
  15. 73
  16. 20
  17. 30
  18. No
  19. 51
  20. Yes
  21. 96
  22. 25
  23. Yes
  24. 9
  25. 60
  26. 53
  27. 105
  28. 24
  29. 40
  30. 70
  31. No
  32. 56
  33. 140
  34. 33
  35. 136
  36. 70
  37. 90
  38. No
  39. 28
  40. 47

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