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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 866 · 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 triangle ABC, angle A = 27° and angle B = 126°. What is angle C (in degrees)?
  2. 2.The two shorter sides of a right-angled triangle are 24 cm and 7 cm. How long is the longest side (in cm)?
  3. 3.The two shorter sides of a right-angled triangle are 18 cm and 24 cm. How long is the longest side (in cm)?
  4. 4.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)?
  5. 5.The angles of a triangle are in the ratio 1 : 1 : 2. What is the biggest angle (in degrees)?
  6. 6.In triangle ABC, angle A = 44° and angle B = 67°. What is angle C (in degrees)?
  7. 7.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)?
  8. 8.In triangle ABC, angle A = 36° and angle B = 59°. What is angle C (in degrees)?
  9. 9.In an isosceles triangle, the two equal angles are 30° each. What is the third angle (in degrees)?
  10. 10.In an isosceles triangle, the two equal angles are 49° each. What is the third angle (in degrees)?
  11. 11.In an isosceles triangle, the two equal angles are 59° each. What is the third angle (in degrees)?
  12. 12.Can a triangle have sides of 4 cm, 6 cm and 4 cm? (a) No (b) Yes
  13. 13.The two interior opposite angles of a triangle are 31° and 23°. What is the exterior angle (in degrees)?
  14. 14.The angles of a triangle are in the ratio 5 : 6 : 7. What is the smallest angle (in degrees)?
  15. 15.The two shorter sides of a right-angled triangle are 36 cm and 15 cm. How long is the longest side (in cm)?
  16. 16.The two interior opposite angles of a triangle are 57° and 80°. What is the exterior angle (in degrees)?
  17. 17.An exterior angle of a triangle is 117°. One of its two interior opposite angles is 67°. What is the other one (in degrees)?
  18. 18.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)?
  19. 19.The angles of a triangle are in the ratio 1 : 4 : 5. What is the biggest angle (in degrees)?
  20. 20.Can a triangle have sides of 8 cm, 11 cm and 7 cm? (a) Yes (b) No
  21. 21.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)?
  22. 22.Can a triangle have sides of 2 cm, 13 cm and 9 cm? (a) Yes (b) No
  23. 23.The angles of a triangle are in the ratio 2 : 2 : 5. What is the biggest angle (in degrees)?
  24. 24.Can a triangle have sides of 4 cm, 12 cm and 4 cm? (a) No (b) Yes
  25. 25.An exterior angle of a triangle is 101°. One of its two interior opposite angles is 46°. What is the other one (in degrees)?
  26. 26.The angles of a triangle are in the ratio 1 : 2 : 2. What is the biggest angle (in degrees)?
  27. 27.The angles of a triangle are in the ratio 2 : 7 : 9. What is the biggest angle (in degrees)?
  28. 28.In a right-angled triangle, one of the other two angles is 78°. What is the third angle (in degrees)?
  29. 29.The two interior opposite angles of a triangle are 80° and 68°. What is the exterior angle (in degrees)?
  30. 30.The longest side of a right-angled triangle is 15 cm and one of the other sides is 9 cm. How long is the third side (in cm)?
  31. 31.In a right-angled triangle, one of the other two angles is 61°. What is the third angle (in degrees)?
  32. 32.Can a triangle have sides of 5 cm, 5 cm and 12 cm? (a) Yes (b) No
  33. 33.In a right-angled triangle, one of the other two angles is 12°. What is the third angle (in degrees)?
  34. 34.An exterior angle of a triangle is 90°. One of its two interior opposite angles is 43°. What is the other one (in degrees)?
  35. 35.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)?
  36. 36.An exterior angle of a triangle is 107°. One of its two interior opposite angles is 76°. What is the other one (in degrees)?
  37. 37.The angles of a triangle are in the ratio 1 : 3 : 5. What is the biggest angle (in degrees)?
  38. 38.An exterior angle of a triangle is 77°. One of its two interior opposite angles is 31°. What is the other one (in degrees)?
  39. 39.An exterior angle of a triangle is 77°. One of its two interior opposite angles is 22°. What is the other one (in degrees)?
  40. 40.In a right-angled triangle, one of the other two angles is 34°. What is the third angle (in degrees)?

Answer key

  1. 27
  2. 25
  3. 30
  4. 24
  5. 90
  6. 69
  7. 8
  8. 85
  9. 120
  10. 82
  11. 62
  12. Yes
  13. 54
  14. 50
  15. 39
  16. 137
  17. 50
  18. 24
  19. 90
  20. Yes
  21. 5
  22. No
  23. 100
  24. No
  25. 55
  26. 72
  27. 90
  28. 12
  29. 148
  30. 12
  31. 29
  32. No
  33. 78
  34. 47
  35. 7
  36. 31
  37. 100
  38. 46
  39. 55
  40. 56

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