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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 360 · 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 25 cm and one of the other sides is 24 cm. How long is the third side (in cm)?
  2. 2.The two shorter sides of a right-angled triangle are 15 cm and 8 cm. How long is the longest side (in cm)?
  3. 3.The longest side of a right-angled triangle is 20 cm and one of the other sides is 16 cm. How long is the third side (in cm)?
  4. 4.In an isosceles triangle, the angle between the two equal sides is 116°. What is each of the other two angles (in degrees)?
  5. 5.In triangle ABC, angle A = 49° and angle B = 81°. What is angle C (in degrees)?
  6. 6.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)?
  7. 7.In triangle ABC, angle A = 64° and angle B = 22°. What is angle C (in degrees)?
  8. 8.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)?
  9. 9.In an isosceles triangle, the two equal angles are 33° each. What is the third angle (in degrees)?
  10. 10.In an isosceles triangle, the angle between the two equal sides is 42°. What is each of the other two angles (in degrees)?
  11. 11.The two interior opposite angles of a triangle are 67° and 41°. What is the exterior angle (in degrees)?
  12. 12.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)?
  13. 13.The two interior opposite angles of a triangle are 29° and 61°. What is the exterior angle (in degrees)?
  14. 14.Can a triangle have sides of 12 cm, 4 cm and 9 cm? (a) No (b) Yes
  15. 15.Can a triangle have sides of 6 cm, 9 cm and 6 cm? (a) No (b) Yes
  16. 16.An exterior angle of a triangle is 111°. One of its two interior opposite angles is 66°. What is the other one (in degrees)?
  17. 17.The angles of a triangle are in the ratio 2 : 3 : 4. What is the smallest angle (in degrees)?
  18. 18.Can a triangle have sides of 2 cm, 11 cm and 6 cm? (a) Yes (b) No
  19. 19.In triangle ABC, angle A = 98° and angle B = 29°. What is angle C (in degrees)?
  20. 20.Can a triangle have sides of 22 cm, 11 cm and 6 cm? (a) Yes (b) No
  21. 21.In triangle ABC, angle A = 66° and angle B = 67°. What is angle C (in degrees)?
  22. 22.The two shorter sides of a right-angled triangle are 20 cm and 15 cm. How long is the longest side (in cm)?
  23. 23.Can a triangle have sides of 24 cm, 10 cm and 11 cm? (a) Yes (b) No
  24. 24.In a right-angled triangle, one of the other two angles is 72°. What is the third angle (in degrees)?
  25. 25.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)?
  26. 26.In triangle ABC, angle A = 79° and angle B = 33°. What is angle C (in degrees)?
  27. 27.In an isosceles triangle, the two equal angles are 20° each. What is the third angle (in degrees)?
  28. 28.In triangle ABC, angle A = 52° and angle B = 65°. What is angle C (in degrees)?
  29. 29.In an isosceles triangle, the two equal angles are 65° each. What is the third angle (in degrees)?
  30. 30.An exterior angle of a triangle is 120°. One of its two interior opposite angles is 50°. What is the other one (in degrees)?
  31. 31.The two shorter sides of a right-angled triangle are 8 cm and 6 cm. How long is the longest side (in cm)?
  32. 32.In an isosceles triangle, the two equal angles are 36° each. What is the third angle (in degrees)?
  33. 33.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)?
  34. 34.The angles of a triangle are in the ratio 1 : 4 : 5. What is the smallest angle (in degrees)?
  35. 35.In a right-angled triangle, one of the other two angles is 64°. What is the third angle (in degrees)?
  36. 36.Can a triangle have sides of 7 cm, 3 cm and 5 cm? (a) Yes (b) No
  37. 37.Can a triangle have sides of 5 cm, 10 cm and 10 cm? (a) Yes (b) No
  38. 38.The two shorter sides of a right-angled triangle are 10 cm and 24 cm. How long is the longest side (in cm)?
  39. 39.In triangle ABC, angle A = 89° and angle B = 56°. What is angle C (in degrees)?
  40. 40.In a right-angled triangle, one of the other two angles is 10°. What is the third angle (in degrees)?

Answer key

  1. 7
  2. 17
  3. 12
  4. 32
  5. 50
  6. 15
  7. 94
  8. 12
  9. 114
  10. 69
  11. 108
  12. 10
  13. 90
  14. Yes
  15. Yes
  16. 45
  17. 40
  18. No
  19. 53
  20. No
  21. 47
  22. 25
  23. No
  24. 18
  25. 24
  26. 68
  27. 140
  28. 63
  29. 50
  30. 70
  31. 10
  32. 108
  33. 9
  34. 18
  35. 26
  36. Yes
  37. Yes
  38. 26
  39. 35
  40. 80

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