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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 45 · 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.

NameDateTime takenScore ___ / 40
  1. 1.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)?
  2. 2.In an isosceles triangle, the two equal angles are 79° each. What is the third angle (in degrees)?
  3. 3.The angles of a triangle are in the ratio 1 : 2 : 6. What is the biggest angle (in degrees)?
  4. 4.Can a triangle have sides of 10 cm, 10 cm and 4 cm? (a) Yes (b) No
  5. 5.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)?
  6. 6.In an isosceles triangle, the angle between the two equal sides is 84°. What is each of the other two angles (in degrees)?
  7. 7.An exterior angle of a triangle is 94°. One of its two interior opposite angles is 36°. What is the other one (in degrees)?
  8. 8.In triangle ABC, angle A = 97° and angle B = 49°. What is angle C (in degrees)?
  9. 9.In an isosceles triangle, the angle between the two equal sides is 142°. What is each of the other two angles (in degrees)?
  10. 10.An exterior angle of a triangle is 108°. One of its two interior opposite angles is 29°. What is the other one (in degrees)?
  11. 11.In triangle ABC, angle A = 28° and angle B = 77°. What is angle C (in degrees)?
  12. 12.The angles of a triangle are in the ratio 3 : 5 : 7. What is the smallest angle (in degrees)?
  13. 13.The longest side of a right-angled triangle is 39 cm and one of the other sides is 15 cm. How long is the third side (in cm)?
  14. 14.The two interior opposite angles of a triangle are 28° and 47°. What is the exterior angle (in degrees)?
  15. 15.In a right-angled triangle, one of the other two angles is 56°. What is the third angle (in degrees)?
  16. 16.An exterior angle of a triangle is 61°. One of its two interior opposite angles is 24°. What is the other one (in degrees)?
  17. 17.In an isosceles triangle, the two equal angles are 73° each. What is the third angle (in degrees)?
  18. 18.In triangle ABC, angle A = 45° and angle B = 107°. What is angle C (in degrees)?
  19. 19.The two shorter sides of a right-angled triangle are 15 cm and 8 cm. How long is the longest side (in cm)?
  20. 20.Can a triangle have sides of 15 cm, 3 cm and 9 cm? (a) No (b) Yes
  21. 21.In triangle ABC, angle A = 38° and angle B = 47°. What is angle C (in degrees)?
  22. 22.The angles of a triangle are in the ratio 3 : 3 : 4. What is the biggest angle (in degrees)?
  23. 23.Can a triangle have sides of 7 cm, 7 cm and 8 cm? (a) No (b) Yes
  24. 24.In a right-angled triangle, one of the other two angles is 28°. What is the third angle (in degrees)?
  25. 25.Can a triangle have sides of 9 cm, 21 cm and 8 cm? (a) No (b) Yes
  26. 26.The two shorter sides of a right-angled triangle are 5 cm and 12 cm. How long is the longest side (in cm)?
  27. 27.The angles of a triangle are in the ratio 3 : 4 : 5. What is the smallest angle (in degrees)?
  28. 28.The two shorter sides of a right-angled triangle are 15 cm and 20 cm. How long is the longest side (in cm)?
  29. 29.In a right-angled triangle, one of the other two angles is 65°. What is the third angle (in degrees)?
  30. 30.The two shorter sides of a right-angled triangle are 3 cm and 4 cm. How long is the longest side (in cm)?
  31. 31.An exterior angle of a triangle is 158°. One of its two interior opposite angles is 78°. What is the other one (in degrees)?
  32. 32.Can a triangle have sides of 12 cm, 9 cm and 19 cm? (a) No (b) Yes
  33. 33.In triangle ABC, angle A = 81° and angle B = 64°. What is angle C (in degrees)?
  34. 34.An exterior angle of a triangle is 76°. One of its two interior opposite angles is 53°. What is the other one (in degrees)?
  35. 35.The two interior opposite angles of a triangle are 46° and 30°. What is the exterior angle (in degrees)?
  36. 36.Can a triangle have sides of 7 cm, 9 cm and 9 cm? (a) No (b) Yes
  37. 37.The two shorter sides of a right-angled triangle are 7 cm and 24 cm. How long is the longest side (in cm)?
  38. 38.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)?
  39. 39.The two interior opposite angles of a triangle are 47° and 39°. What is the exterior angle (in degrees)?
  40. 40.The angles of a triangle are in the ratio 2 : 3 : 4. What is the biggest angle (in degrees)?

Answer key

  1. 24
  2. 22
  3. 120
  4. Yes
  5. 5
  6. 48
  7. 58
  8. 34
  9. 19
  10. 79
  11. 75
  12. 36
  13. 36
  14. 75
  15. 34
  16. 37
  17. 34
  18. 28
  19. 17
  20. No
  21. 95
  22. 72
  23. Yes
  24. 62
  25. No
  26. 13
  27. 45
  28. 25
  29. 25
  30. 5
  31. 80
  32. Yes
  33. 35
  34. 23
  35. 76
  36. Yes
  37. 25
  38. 10
  39. 86
  40. 80

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