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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 42 · 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.An exterior angle of a triangle is 70°. One of its two interior opposite angles is 31°. What is the other one (in degrees)?
  2. 2.An exterior angle of a triangle is 111°. One of its two interior opposite angles is 75°. What is the other one (in degrees)?
  3. 3.In an isosceles triangle, the two equal angles are 34° each. What is the third angle (in degrees)?
  4. 4.In an isosceles triangle, the angle between the two equal sides is 128°. What is each of the other two angles (in degrees)?
  5. 5.In triangle ABC, angle A = 53° and angle B = 35°. What is angle C (in degrees)?
  6. 6.In triangle ABC, angle A = 80° and angle B = 29°. What is angle C (in degrees)?
  7. 7.Can a triangle have sides of 10 cm, 21 cm and 10 cm? (a) Yes (b) No
  8. 8.The two shorter sides of a right-angled triangle are 15 cm and 36 cm. How long is the longest side (in cm)?
  9. 9.The angles of a triangle are in the ratio 1 : 2 : 3. What is the biggest angle (in degrees)?
  10. 10.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)?
  11. 11.In an isosceles triangle, the angle between the two equal sides is 36°. What is each of the other two angles (in degrees)?
  12. 12.The two interior opposite angles of a triangle are 54° and 78°. What is the exterior angle (in degrees)?
  13. 13.In a right-angled triangle, one of the other two angles is 61°. What is the third angle (in degrees)?
  14. 14.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)?
  15. 15.The two shorter sides of a right-angled triangle are 3 cm and 4 cm. How long is the longest side (in cm)?
  16. 16.In an isosceles triangle, the angle between the two equal sides is 158°. What is each of the other two angles (in degrees)?
  17. 17.Can a triangle have sides of 9 cm, 15 cm and 9 cm? (a) No (b) Yes
  18. 18.In triangle ABC, angle A = 64° and angle B = 34°. What is angle C (in degrees)?
  19. 19.The angles of a triangle are in the ratio 2 : 7 : 9. What is the smallest angle (in degrees)?
  20. 20.In triangle ABC, angle A = 48° and angle B = 81°. What is angle C (in degrees)?
  21. 21.In an isosceles triangle, the angle between the two equal sides is 24°. What is each of the other two angles (in degrees)?
  22. 22.The two interior opposite angles of a triangle are 43° and 39°. What is the exterior angle (in degrees)?
  23. 23.In an isosceles triangle, the angle between the two equal sides is 48°. What is each of the other two angles (in degrees)?
  24. 24.The two shorter sides of a right-angled triangle are 18 cm and 24 cm. How long is the longest side (in cm)?
  25. 25.In triangle ABC, angle A = 99° and angle B = 32°. What is angle C (in degrees)?
  26. 26.An exterior angle of a triangle is 70°. One of its two interior opposite angles is 38°. What is the other one (in degrees)?
  27. 27.The two interior opposite angles of a triangle are 65° and 37°. What is the exterior angle (in degrees)?
  28. 28.The two interior opposite angles of a triangle are 63° and 58°. What is the exterior angle (in degrees)?
  29. 29.The longest side of a right-angled triangle is 25 cm and one of the other sides is 20 cm. How long is the third side (in cm)?
  30. 30.In a right-angled triangle, one of the other two angles is 60°. What is the third angle (in degrees)?
  31. 31.The angles of a triangle are in the ratio 3 : 5 : 7. What is the smallest angle (in degrees)?
  32. 32.Can a triangle have sides of 22 cm, 9 cm and 12 cm? (a) No (b) Yes
  33. 33.An exterior angle of a triangle is 109°. One of its two interior opposite angles is 34°. What is the other one (in degrees)?
  34. 34.In a right-angled triangle, one of the other two angles is 72°. What is the third angle (in degrees)?
  35. 35.In triangle ABC, angle A = 75° and angle B = 75°. What is angle C (in degrees)?
  36. 36.In an isosceles triangle, the angle between the two equal sides is 132°. What is each of the other two angles (in degrees)?
  37. 37.Can a triangle have sides of 7 cm, 8 cm and 3 cm? (a) Yes (b) No
  38. 38.In triangle ABC, angle A = 41° and angle B = 55°. What is angle C (in degrees)?
  39. 39.In triangle ABC, angle A = 80° and angle B = 61°. What is angle C (in degrees)?
  40. 40.The two shorter sides of a right-angled triangle are 7 cm and 24 cm. How long is the longest side (in cm)?

Answer key

  1. 39
  2. 36
  3. 112
  4. 26
  5. 92
  6. 71
  7. No
  8. 39
  9. 90
  10. 7
  11. 72
  12. 132
  13. 29
  14. 20
  15. 5
  16. 11
  17. Yes
  18. 82
  19. 20
  20. 51
  21. 78
  22. 82
  23. 66
  24. 30
  25. 49
  26. 32
  27. 102
  28. 121
  29. 15
  30. 30
  31. 36
  32. No
  33. 75
  34. 18
  35. 30
  36. 24
  37. Yes
  38. 84
  39. 39
  40. 25

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