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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 117 · 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 1 : 2 : 2. What is the smallest angle (in degrees)?
  2. 2.Can a triangle have sides of 10 cm, 12 cm and 3 cm? (a) No (b) Yes
  3. 3.Can a triangle have sides of 7 cm, 9 cm and 18 cm? (a) No (b) Yes
  4. 4.In an isosceles triangle, the angle between the two equal sides is 158°. What is each of the other two angles (in degrees)?
  5. 5.In triangle ABC, angle A = 22° and angle B = 38°. What is angle C (in degrees)?
  6. 6.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles (in degrees)?
  7. 7.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)?
  8. 8.An exterior angle of a triangle is 60°. One of its two interior opposite angles is 26°. What is the other one (in degrees)?
  9. 9.In a right-angled triangle, one of the other two angles is 57°. What is the third angle (in degrees)?
  10. 10.Can a triangle have sides of 6 cm, 16 cm and 10 cm? (a) No (b) Yes
  11. 11.In an isosceles triangle, the two equal angles are 33° each. What is the third angle (in degrees)?
  12. 12.The angles of a triangle are in the ratio 1 : 4 : 5. What is the smallest angle (in degrees)?
  13. 13.In a right-angled triangle, one of the other two angles is 39°. What is the third angle (in degrees)?
  14. 14.In triangle ABC, angle A = 58° and angle B = 79°. What is angle C (in degrees)?
  15. 15.The angles of a triangle are in the ratio 2 : 7 : 9. What is the biggest angle (in degrees)?
  16. 16.In an isosceles triangle, the two equal angles are 37° each. What is the third angle (in degrees)?
  17. 17.In a right-angled triangle, one of the other two angles is 37°. What is the third angle (in degrees)?
  18. 18.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)?
  19. 19.In an isosceles triangle, the two equal angles are 67° each. What is the third angle (in degrees)?
  20. 20.An exterior angle of a triangle is 134°. One of its two interior opposite angles is 61°. What is the other one (in degrees)?
  21. 21.An exterior angle of a triangle is 57°. One of its two interior opposite angles is 37°. What is the other one (in degrees)?
  22. 22.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)?
  23. 23.In an isosceles triangle, the angle between the two equal sides is 148°. What is each of the other two angles (in degrees)?
  24. 24.In triangle ABC, angle A = 57° and angle B = 97°. What is angle C (in degrees)?
  25. 25.In triangle ABC, angle A = 98° and angle B = 30°. What is angle C (in degrees)?
  26. 26.The two shorter sides of a right-angled triangle are 8 cm and 15 cm. How long is the longest side (in cm)?
  27. 27.In an isosceles triangle, the two equal angles are 81° each. What is the third angle (in degrees)?
  28. 28.In a right-angled triangle, one of the other two angles is 26°. What is the third angle (in degrees)?
  29. 29.An exterior angle of a triangle is 119°. One of its two interior opposite angles is 72°. What is the other one (in degrees)?
  30. 30.The angles of a triangle are in the ratio 1 : 2 : 6. What is the biggest angle (in degrees)?
  31. 31.Can a triangle have sides of 10 cm, 12 cm and 10 cm? (a) No (b) Yes
  32. 32.In an isosceles triangle, the two equal angles are 56° each. What is the third angle (in degrees)?
  33. 33.Can a triangle have sides of 3 cm, 1 cm and 3 cm? (a) Yes (b) No
  34. 34.An exterior angle of a triangle is 144°. One of its two interior opposite angles is 72°. What is the other one (in degrees)?
  35. 35.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)?
  36. 36.In triangle ABC, angle A = 98° and angle B = 22°. What is angle C (in degrees)?
  37. 37.An exterior angle of a triangle is 99°. One of its two interior opposite angles is 21°. What is the other one (in degrees)?
  38. 38.In an isosceles triangle, the two equal angles are 30° each. What is the third angle (in degrees)?
  39. 39.In a right-angled triangle, one of the other two angles is 53°. What is the third angle (in degrees)?
  40. 40.In triangle ABC, angle A = 36° and angle B = 31°. What is angle C (in degrees)?

Answer key

  1. 36
  2. Yes
  3. No
  4. 11
  5. 120
  6. 50
  7. 5
  8. 34
  9. 33
  10. No
  11. 114
  12. 18
  13. 51
  14. 43
  15. 90
  16. 106
  17. 53
  18. 24
  19. 46
  20. 73
  21. 20
  22. 16
  23. 16
  24. 26
  25. 52
  26. 17
  27. 18
  28. 64
  29. 47
  30. 120
  31. Yes
  32. 68
  33. Yes
  34. 72
  35. 15
  36. 60
  37. 78
  38. 120
  39. 37
  40. 113

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