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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 118 · 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.In a right-angled triangle, one of the other two angles is 54°. What is the third angle (in degrees)?
  2. 2.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)?
  3. 3.An exterior angle of a triangle is 78°. One of its two interior opposite angles is 50°. What is the other one (in degrees)?
  4. 4.An exterior angle of a triangle is 106°. One of its two interior opposite angles is 39°. What is the other one (in degrees)?
  5. 5.Can a triangle have sides of 4 cm, 3 cm and 3 cm? (a) Yes (b) No
  6. 6.Can a triangle have sides of 3 cm, 3 cm and 5 cm? (a) Yes (b) No
  7. 7.The angles of a triangle are in the ratio 1 : 4 : 5. What is the biggest angle (in degrees)?
  8. 8.Can a triangle have sides of 18 cm, 9 cm and 10 cm? (a) Yes (b) No
  9. 9.In triangle ABC, angle A = 36° and angle B = 45°. What is angle C (in degrees)?
  10. 10.The two shorter sides of a right-angled triangle are 7 cm and 24 cm. How long is the longest side (in cm)?
  11. 11.In an isosceles triangle, the angle between the two equal sides is 26°. What is each of the other two angles (in degrees)?
  12. 12.The angles of a triangle are in the ratio 2 : 3 : 4. What is the smallest angle (in degrees)?
  13. 13.The two interior opposite angles of a triangle are 67° and 63°. What is the exterior angle (in degrees)?
  14. 14.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)?
  15. 15.Can a triangle have sides of 5 cm, 8 cm and 4 cm? (a) Yes (b) No
  16. 16.An exterior angle of a triangle is 144°. One of its two interior opposite angles is 72°. What is the other one (in degrees)?
  17. 17.An exterior angle of a triangle is 125°. One of its two interior opposite angles is 76°. What is the other one (in degrees)?
  18. 18.An exterior angle of a triangle is 55°. One of its two interior opposite angles is 30°. What is the other one (in degrees)?
  19. 19.The two interior opposite angles of a triangle are 52° and 38°. What is the exterior angle (in degrees)?
  20. 20.The angles of a triangle are in the ratio 5 : 6 : 7. What is the biggest angle (in degrees)?
  21. 21.The angles of a triangle are in the ratio 1 : 4 : 5. What is the smallest angle (in degrees)?
  22. 22.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)?
  23. 23.In an isosceles triangle, the two equal angles are 72° each. What is the third angle (in degrees)?
  24. 24.The two shorter sides of a right-angled triangle are 15 cm and 36 cm. How long is the longest side (in cm)?
  25. 25.The angles of a triangle are in the ratio 3 : 3 : 4. What is the smallest angle (in degrees)?
  26. 26.In an isosceles triangle, the two equal angles are 23° each. What is the third angle (in degrees)?
  27. 27.The angles of a triangle are in the ratio 3 : 4 : 5. What is the biggest angle (in degrees)?
  28. 28.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)?
  29. 29.The two interior opposite angles of a triangle are 80° and 34°. What is the exterior angle (in degrees)?
  30. 30.The angles of a triangle are in the ratio 1 : 2 : 6. What is the smallest angle (in degrees)?
  31. 31.In a right-angled triangle, one of the other two angles is 66°. What is the third angle (in degrees)?
  32. 32.Can a triangle have sides of 5 cm, 5 cm and 7 cm? (a) Yes (b) No
  33. 33.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)?
  34. 34.The two shorter sides of a right-angled triangle are 24 cm and 10 cm. How long is the longest side (in cm)?
  35. 35.Can a triangle have sides of 8 cm, 7 cm and 18 cm? (a) Yes (b) No
  36. 36.In an isosceles triangle, the angle between the two equal sides is 84°. What is each of the other two angles (in degrees)?
  37. 37.Can a triangle have sides of 2 cm, 8 cm and 2 cm? (a) Yes (b) No
  38. 38.In an isosceles triangle, the two equal angles are 68° each. What is the third angle (in degrees)?
  39. 39.The two shorter sides of a right-angled triangle are 20 cm and 15 cm. How long is the longest side (in cm)?
  40. 40.In triangle ABC, angle A = 39° and angle B = 34°. What is angle C (in degrees)?

Answer key

  1. 36
  2. 3
  3. 28
  4. 67
  5. Yes
  6. Yes
  7. 90
  8. Yes
  9. 99
  10. 25
  11. 77
  12. 40
  13. 130
  14. 24
  15. Yes
  16. 72
  17. 49
  18. 25
  19. 90
  20. 70
  21. 18
  22. 8
  23. 36
  24. 39
  25. 54
  26. 134
  27. 75
  28. 24
  29. 114
  30. 20
  31. 24
  32. Yes
  33. 8
  34. 26
  35. No
  36. 48
  37. No
  38. 44
  39. 25
  40. 107

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