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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 944 · 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 two shorter sides of a right-angled triangle are 3 cm and 4 cm. How long is the longest 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 25 cm and one of the other sides is 7 cm. How long is the third side (in cm)?
  4. 4.The two interior opposite angles of a triangle are 27° and 35°. What is the exterior angle (in degrees)?
  5. 5.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles (in degrees)?
  6. 6.The angles of a triangle are in the ratio 2 : 3 : 4. What is the biggest angle (in degrees)?
  7. 7.In a right-angled triangle, one of the other two angles is 38°. What is the third angle (in degrees)?
  8. 8.In triangle ABC, angle A = 96° and angle B = 63°. What is angle C (in degrees)?
  9. 9.In a right-angled triangle, one of the other two angles is 30°. What is the third angle (in degrees)?
  10. 10.The angles of a triangle are in the ratio 1 : 2 : 2. What is the smallest angle (in degrees)?
  11. 11.In triangle ABC, angle A = 95° and angle B = 58°. What is angle C (in degrees)?
  12. 12.Can a triangle have sides of 9 cm, 8 cm and 2 cm? (a) Yes (b) No
  13. 13.The longest side of a right-angled triangle is 10 cm and one of the other sides is 8 cm. How long is the third side (in cm)?
  14. 14.In an isosceles triangle, the angle between the two equal sides is 62°. What is each of the other two angles (in degrees)?
  15. 15.The longest side of a right-angled triangle is 30 cm and one of the other sides is 18 cm. How long is the third side (in cm)?
  16. 16.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)?
  17. 17.The longest side of a right-angled triangle is 20 cm and one of the other sides is 12 cm. How long is the third side (in cm)?
  18. 18.In a right-angled triangle, one of the other two angles is 64°. What is the third angle (in degrees)?
  19. 19.The two interior opposite angles of a triangle are 20° and 42°. What is the exterior angle (in degrees)?
  20. 20.In an isosceles triangle, the two equal angles are 81° each. What is the third angle (in degrees)?
  21. 21.In a right-angled triangle, one of the other two angles is 34°. What is the third angle (in degrees)?
  22. 22.In a right-angled triangle, one of the other two angles is 16°. What is the third angle (in degrees)?
  23. 23.In a right-angled triangle, one of the other two angles is 58°. What is the third angle (in degrees)?
  24. 24.Can a triangle have sides of 11 cm, 6 cm and 4 cm? (a) No (b) Yes
  25. 25.In an isosceles triangle, the angle between the two equal sides is 68°. What is each of the other two angles (in degrees)?
  26. 26.The angles of a triangle are in the ratio 1 : 2 : 6. What is the biggest angle (in degrees)?
  27. 27.In an isosceles triangle, the two equal angles are 70° each. What is the third angle (in degrees)?
  28. 28.The angles of a triangle are in the ratio 1 : 2 : 2. What is the biggest angle (in degrees)?
  29. 29.The angles of a triangle are in the ratio 1 : 2 : 6. What is the smallest angle (in degrees)?
  30. 30.In a right-angled triangle, one of the other two angles is 80°. What is the third angle (in degrees)?
  31. 31.In an isosceles triangle, the angle between the two equal sides is 152°. What is each of the other two angles (in degrees)?
  32. 32.The angles of a triangle are in the ratio 4 : 5 : 6. What is the smallest angle (in degrees)?
  33. 33.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)?
  34. 34.The angles of a triangle are in the ratio 2 : 7 : 9. What is the smallest angle (in degrees)?
  35. 35.An exterior angle of a triangle is 75°. One of its two interior opposite angles is 33°. What is the other one (in degrees)?
  36. 36.The angles of a triangle are in the ratio 5 : 6 : 7. What is the smallest angle (in degrees)?
  37. 37.Can a triangle have sides of 8 cm, 3 cm and 7 cm? (a) No (b) Yes
  38. 38.Can a triangle have sides of 22 cm, 9 cm and 9 cm? (a) No (b) Yes
  39. 39.In a right-angled triangle, one of the other two angles is 15°. What is the third angle (in degrees)?
  40. 40.An exterior angle of a triangle is 96°. One of its two interior opposite angles is 76°. What is the other one (in degrees)?

Answer key

  1. 5
  2. 17
  3. 24
  4. 62
  5. 65
  6. 80
  7. 52
  8. 21
  9. 60
  10. 36
  11. 27
  12. Yes
  13. 6
  14. 59
  15. 24
  16. 12
  17. 16
  18. 26
  19. 62
  20. 18
  21. 56
  22. 74
  23. 32
  24. No
  25. 56
  26. 120
  27. 40
  28. 72
  29. 20
  30. 10
  31. 14
  32. 48
  33. 15
  34. 20
  35. 42
  36. 50
  37. Yes
  38. No
  39. 75
  40. 20

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