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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 902 · 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 angles of a triangle are in the ratio 3 : 5 : 7. What is the smallest angle (in degrees)?
  2. 2.In a right-angled triangle, one of the other two angles is 34°. What is the third angle (in degrees)?
  3. 3.An exterior angle of a triangle is 52°. One of its two interior opposite angles is 24°. What is the other one (in degrees)?
  4. 4.The angles of a triangle are in the ratio 1 : 2 : 3. What is the smallest angle (in degrees)?
  5. 5.In a right-angled triangle, one of the other two angles is 60°. What is the third 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.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)?
  8. 8.In a right-angled triangle, one of the other two angles is 57°. What is the third angle (in degrees)?
  9. 9.The two shorter sides of a right-angled triangle are 24 cm and 18 cm. How long is the longest side (in cm)?
  10. 10.In triangle ABC, angle A = 29° and angle B = 81°. What is angle C (in degrees)?
  11. 11.In triangle ABC, angle A = 77° and angle B = 82°. What is angle C (in degrees)?
  12. 12.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)?
  13. 13.In an isosceles triangle, the two equal angles are 61° each. What is the third angle (in degrees)?
  14. 14.The angles of a triangle are in the ratio 1 : 2 : 3. What is the biggest angle (in degrees)?
  15. 15.The two interior opposite angles of a triangle are 53° and 77°. What is the exterior angle (in degrees)?
  16. 16.In a right-angled triangle, one of the other two angles is 40°. What is the third angle (in degrees)?
  17. 17.In an isosceles triangle, the two equal angles are 42° each. What is the third angle (in degrees)?
  18. 18.In an isosceles triangle, the angle between the two equal sides is 132°. What is each of the other two angles (in degrees)?
  19. 19.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)?
  20. 20.In triangle ABC, angle A = 61° and angle B = 36°. What is angle C (in degrees)?
  21. 21.The angles of a triangle are in the ratio 2 : 3 : 4. What is the biggest angle (in degrees)?
  22. 22.Can a triangle have sides of 17 cm, 7 cm and 7 cm? (a) No (b) Yes
  23. 23.In triangle ABC, angle A = 52° and angle B = 30°. What is angle C (in degrees)?
  24. 24.In an isosceles triangle, the two equal angles are 37° each. What is the third angle (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.The angles of a triangle are in the ratio 2 : 3 : 5. What is the biggest angle (in degrees)?
  27. 27.In a right-angled triangle, one of the other two angles is 33°. What is the third angle (in degrees)?
  28. 28.In triangle ABC, angle A = 26° and angle B = 64°. What is angle C (in degrees)?
  29. 29.The two shorter sides of a right-angled triangle are 12 cm and 5 cm. How long is the longest side (in cm)?
  30. 30.In triangle ABC, angle A = 54° and angle B = 41°. What is angle C (in degrees)?
  31. 31.In triangle ABC, angle A = 32° and angle B = 77°. What is angle C (in degrees)?
  32. 32.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)?
  33. 33.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)?
  34. 34.An exterior angle of a triangle is 103°. One of its two interior opposite angles is 24°. What is the other one (in degrees)?
  35. 35.The angles of a triangle are in the ratio 1 : 2 : 2. What is the smallest angle (in degrees)?
  36. 36.The two shorter sides of a right-angled triangle are 3 cm and 4 cm. How long is the longest side (in cm)?
  37. 37.Can a triangle have sides of 11 cm, 25 cm and 10 cm? (a) Yes (b) No
  38. 38.In an isosceles triangle, the two equal angles are 28° each. What is the third angle (in degrees)?
  39. 39.The longest side of a right-angled triangle is 10 cm and one of the other sides is 6 cm. How long is the third side (in cm)?
  40. 40.In triangle ABC, angle A = 86° and angle B = 72°. What is angle C (in degrees)?

Answer key

  1. 36
  2. 56
  3. 28
  4. 30
  5. 30
  6. 48
  7. 7
  8. 33
  9. 30
  10. 70
  11. 21
  12. 12
  13. 58
  14. 90
  15. 130
  16. 50
  17. 96
  18. 24
  19. 9
  20. 83
  21. 80
  22. No
  23. 98
  24. 106
  25. 8
  26. 90
  27. 57
  28. 90
  29. 13
  30. 85
  31. 71
  32. 24
  33. 10
  34. 79
  35. 36
  36. 5
  37. No
  38. 124
  39. 8
  40. 22

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