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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 951 · 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 52°. What is the third angle (in degrees)?
  2. 2.The angles of a triangle are in the ratio 5 : 6 : 7. What is the smallest angle (in degrees)?
  3. 3.The angles of a triangle are in the ratio 2 : 7 : 9. What is the smallest angle (in degrees)?
  4. 4.The angles of a triangle are in the ratio 1 : 1 : 2. What is the smallest angle (in degrees)?
  5. 5.The angles of a triangle are in the ratio 3 : 4 : 5. What is the biggest angle (in degrees)?
  6. 6.In a right-angled triangle, one of the other two angles is 42°. What is the third angle (in degrees)?
  7. 7.Can a triangle have sides of 11 cm, 6 cm and 6 cm? (a) No (b) Yes
  8. 8.An exterior angle of a triangle is 109°. One of its two interior opposite angles is 39°. What is the other one (in degrees)?
  9. 9.The two shorter sides of a right-angled triangle are 12 cm and 5 cm. How long is the longest side (in cm)?
  10. 10.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)?
  11. 11.In a right-angled triangle, one of the other two angles is 27°. What is the third angle (in degrees)?
  12. 12.Can a triangle have sides of 6 cm, 18 cm and 8 cm? (a) No (b) Yes
  13. 13.The two shorter sides of a right-angled triangle are 7 cm and 24 cm. How long is the longest side (in cm)?
  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.In an isosceles triangle, the angle between the two equal sides is 82°. What is each of the other two angles (in degrees)?
  16. 16.In a right-angled triangle, one of the other two angles is 60°. What is the third angle (in degrees)?
  17. 17.The two interior opposite angles of a triangle are 74° and 78°. What is the exterior angle (in degrees)?
  18. 18.In a right-angled triangle, one of the other two angles is 63°. What is the third angle (in degrees)?
  19. 19.In a right-angled triangle, one of the other two angles is 64°. What is the third angle (in degrees)?
  20. 20.In triangle ABC, angle A = 57° and angle B = 78°. What is angle C (in degrees)?
  21. 21.In an isosceles triangle, the two equal angles are 37° each. What is the third angle (in degrees)?
  22. 22.The angles of a triangle are in the ratio 2 : 3 : 5. What is the biggest angle (in degrees)?
  23. 23.The two shorter sides of a right-angled triangle are 6 cm and 8 cm. How long is the longest side (in cm)?
  24. 24.An exterior angle of a triangle is 68°. One of its two interior opposite angles is 31°. What is the other one (in degrees)?
  25. 25.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)?
  26. 26.In a right-angled triangle, one of the other two angles is 62°. What is the third angle (in degrees)?
  27. 27.In an isosceles triangle, the two equal angles are 79° each. What is the third angle (in degrees)?
  28. 28.In an isosceles triangle, the angle between the two equal sides is 44°. What is each of the other two angles (in degrees)?
  29. 29.In triangle ABC, angle A = 79° and angle B = 44°. What is angle C (in degrees)?
  30. 30.In triangle ABC, angle A = 80° and angle B = 31°. What is angle C (in degrees)?
  31. 31.The two interior opposite angles of a triangle are 28° and 37°. What is the exterior angle (in degrees)?
  32. 32.The two shorter sides of a right-angled triangle are 20 cm and 15 cm. How long is the longest side (in cm)?
  33. 33.In an isosceles triangle, the two equal angles are 46° each. What is the third angle (in degrees)?
  34. 34.The two interior opposite angles of a triangle are 57° and 28°. What is the exterior angle (in degrees)?
  35. 35.Can a triangle have sides of 12 cm, 4 cm and 5 cm? (a) No (b) Yes
  36. 36.An exterior angle of a triangle is 63°. One of its two interior opposite angles is 25°. What is the other one (in degrees)?
  37. 37.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)?
  38. 38.The two shorter sides of a right-angled triangle are 8 cm and 15 cm. How long is the longest side (in cm)?
  39. 39.The two interior opposite angles of a triangle are 24° and 30°. What is the exterior angle (in degrees)?
  40. 40.Can a triangle have sides of 14 cm, 5 cm and 4 cm? (a) Yes (b) No

Answer key

  1. 38
  2. 50
  3. 20
  4. 45
  5. 75
  6. 48
  7. Yes
  8. 70
  9. 13
  10. 20
  11. 63
  12. No
  13. 25
  14. 24
  15. 49
  16. 30
  17. 152
  18. 27
  19. 26
  20. 45
  21. 106
  22. 90
  23. 10
  24. 37
  25. 8
  26. 28
  27. 22
  28. 68
  29. 57
  30. 69
  31. 65
  32. 25
  33. 88
  34. 85
  35. No
  36. 38
  37. 12
  38. 17
  39. 54
  40. No

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