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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 523 · 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 103°. One of its two interior opposite angles is 32°. What is the other one (in degrees)?
  2. 2.The angles of a triangle are in the ratio 2 : 3 : 5. What is the biggest angle (in degrees)?
  3. 3.In an isosceles triangle, the angle between the two equal sides is 114°. What is each of the other two angles (in degrees)?
  4. 4.In triangle ABC, angle A = 58° and angle B = 86°. What is angle C (in degrees)?
  5. 5.The two interior opposite angles of a triangle are 21° and 72°. What is the exterior angle (in degrees)?
  6. 6.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)?
  7. 7.An exterior angle of a triangle is 111°. One of its two interior opposite angles is 38°. What is the other one (in degrees)?
  8. 8.In a right-angled triangle, one of the other two angles is 33°. What is the third angle (in degrees)?
  9. 9.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)?
  10. 10.In an isosceles triangle, the two equal angles are 73° each. What is the third angle (in degrees)?
  11. 11.The angles of a triangle are in the ratio 5 : 6 : 7. What is the biggest angle (in degrees)?
  12. 12.The angles of a triangle are in the ratio 3 : 5 : 7. What is the biggest angle (in degrees)?
  13. 13.In an isosceles triangle, the two equal angles are 79° each. What is the third angle (in degrees)?
  14. 14.An exterior angle of a triangle is 114°. One of its two interior opposite angles is 51°. What is the other one (in degrees)?
  15. 15.In an isosceles triangle, the two equal angles are 32° each. What is the third angle (in degrees)?
  16. 16.In an isosceles triangle, the angle between the two equal sides is 88°. What is each of the other two angles (in degrees)?
  17. 17.The two interior opposite angles of a triangle are 42° and 62°. What is the exterior angle (in degrees)?
  18. 18.The two shorter sides of a right-angled triangle are 24 cm and 7 cm. How long is the longest side (in cm)?
  19. 19.In a right-angled triangle, one of the other two angles is 23°. What is the third angle (in degrees)?
  20. 20.In triangle ABC, angle A = 72° and angle B = 79°. What is angle C (in degrees)?
  21. 21.In an isosceles triangle, the two equal angles are 62° each. What is the third angle (in degrees)?
  22. 22.An exterior angle of a triangle is 97°. One of its two interior opposite angles is 25°. What is the other one (in degrees)?
  23. 23.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)?
  24. 24.In a right-angled triangle, one of the other two angles is 27°. What is the third angle (in degrees)?
  25. 25.In triangle ABC, angle A = 42° and angle B = 27°. What is angle C (in degrees)?
  26. 26.In a right-angled triangle, one of the other two angles is 80°. What is the third angle (in degrees)?
  27. 27.The angles of a triangle are in the ratio 1 : 3 : 5. What is the smallest angle (in degrees)?
  28. 28.Can a triangle have sides of 10 cm, 19 cm and 9 cm? (a) Yes (b) No
  29. 29.Can a triangle have sides of 7 cm, 6 cm and 10 cm? (a) No (b) Yes
  30. 30.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)?
  31. 31.In an isosceles triangle, the angle between the two equal sides is 128°. What is each of the other two angles (in degrees)?
  32. 32.The two interior opposite angles of a triangle are 61° and 78°. What is the exterior angle (in degrees)?
  33. 33.In triangle ABC, angle A = 57° and angle B = 79°. What is angle C (in degrees)?
  34. 34.An exterior angle of a triangle is 106°. One of its two interior opposite angles is 44°. What is the other one (in degrees)?
  35. 35.Can a triangle have sides of 5 cm, 14 cm and 5 cm? (a) No (b) Yes
  36. 36.Can a triangle have sides of 2 cm, 8 cm and 15 cm? (a) Yes (b) No
  37. 37.In an isosceles triangle, the angle between the two equal sides is 54°. What is each of the other two angles (in degrees)?
  38. 38.Can a triangle have sides of 10 cm, 11 cm and 15 cm? (a) Yes (b) No
  39. 39.The angles of a triangle are in the ratio 1 : 2 : 3. What is the smallest angle (in degrees)?
  40. 40.An exterior angle of a triangle is 78°. One of its two interior opposite angles is 38°. What is the other one (in degrees)?

Answer key

  1. 71
  2. 90
  3. 33
  4. 36
  5. 93
  6. 24
  7. 73
  8. 57
  9. 15
  10. 34
  11. 70
  12. 84
  13. 22
  14. 63
  15. 116
  16. 46
  17. 104
  18. 25
  19. 67
  20. 29
  21. 56
  22. 72
  23. 7
  24. 63
  25. 111
  26. 10
  27. 20
  28. No
  29. Yes
  30. 8
  31. 26
  32. 139
  33. 44
  34. 62
  35. No
  36. No
  37. 63
  38. Yes
  39. 30
  40. 40

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