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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 606 · 40 sums
TalentJR

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.In a right-angled triangle, one of the other two angles is 47°. What is the third angle (in degrees)?
  2. 2.In an isosceles triangle, the two equal angles are 29° each. What is the third angle (in degrees)?
  3. 3.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)?
  4. 4.The two interior opposite angles of a triangle are 57° and 31°. What is the exterior 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.The angles of a triangle are in the ratio 1 : 4 : 5. What is the biggest angle (in degrees)?
  7. 7.In a right-angled triangle, one of the other two angles is 27°. What is the third angle (in degrees)?
  8. 8.The angles of a triangle are in the ratio 1 : 3 : 5. What is the smallest angle (in degrees)?
  9. 9.The angles of a triangle are in the ratio 1 : 1 : 2. What is the smallest angle (in degrees)?
  10. 10.In a right-angled triangle, one of the other two angles is 11°. What is the third angle (in degrees)?
  11. 11.The angles of a triangle are in the ratio 1 : 2 : 3. What is the biggest angle (in degrees)?
  12. 12.The angles of a triangle are in the ratio 2 : 7 : 9. What is the biggest angle (in degrees)?
  13. 13.The angles of a triangle are in the ratio 1 : 1 : 2. What is the biggest angle (in degrees)?
  14. 14.In a right-angled triangle, one of the other two angles is 22°. What is the third angle (in degrees)?
  15. 15.In a right-angled triangle, one of the other two angles is 61°. What is the third angle (in degrees)?
  16. 16.In triangle ABC, angle A = 78° and angle B = 77°. What is angle C (in degrees)?
  17. 17.The two interior opposite angles of a triangle are 34° and 45°. What is the exterior angle (in degrees)?
  18. 18.In triangle ABC, angle A = 35° and angle B = 39°. What is angle C (in degrees)?
  19. 19.The two shorter sides of a right-angled triangle are 6 cm and 8 cm. How long is the longest side (in cm)?
  20. 20.In triangle ABC, angle A = 76° and angle B = 81°. What is angle C (in degrees)?
  21. 21.In an isosceles triangle, the two equal angles are 72° each. What is the third angle (in degrees)?
  22. 22.In triangle ABC, angle A = 75° and angle B = 74°. What is angle C (in degrees)?
  23. 23.The angles of a triangle are in the ratio 4 : 5 : 6. What is the smallest angle (in degrees)?
  24. 24.The angles of a triangle are in the ratio 3 : 4 : 5. What is the smallest angle (in degrees)?
  25. 25.The angles of a triangle are in the ratio 1 : 3 : 5. What is the biggest angle (in degrees)?
  26. 26.The angles of a triangle are in the ratio 4 : 5 : 6. What is the biggest angle (in degrees)?
  27. 27.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)?
  28. 28.In an isosceles triangle, the angle between the two equal sides is 108°. What is each of the other two angles (in degrees)?
  29. 29.In a right-angled triangle, one of the other two angles is 56°. What is the third angle (in degrees)?
  30. 30.Can a triangle have sides of 10 cm, 5 cm and 11 cm? (a) Yes (b) No
  31. 31.In triangle ABC, angle A = 48° and angle B = 95°. What is angle C (in degrees)?
  32. 32.In an isosceles triangle, the two equal angles are 43° each. What is the third angle (in degrees)?
  33. 33.In an isosceles triangle, the angle between the two equal sides is 124°. What is each of the other two angles (in degrees)?
  34. 34.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles (in degrees)?
  35. 35.Can a triangle have sides of 12 cm, 5 cm and 10 cm? (a) No (b) Yes
  36. 36.An exterior angle of a triangle is 87°. One of its two interior opposite angles is 53°. What is the other one (in degrees)?
  37. 37.An exterior angle of a triangle is 87°. One of its two interior opposite angles is 42°. What is the other one (in degrees)?
  38. 38.In a right-angled triangle, one of the other two angles is 13°. What is the third angle (in degrees)?
  39. 39.In a right-angled triangle, one of the other two angles is 19°. What is the third angle (in degrees)?
  40. 40.In an isosceles triangle, the two equal angles are 81° each. What is the third angle (in degrees)?

Answer key

  1. 43
  2. 122
  3. 5
  4. 88
  5. 30
  6. 90
  7. 63
  8. 20
  9. 45
  10. 79
  11. 90
  12. 90
  13. 90
  14. 68
  15. 29
  16. 25
  17. 79
  18. 106
  19. 10
  20. 23
  21. 36
  22. 31
  23. 48
  24. 45
  25. 100
  26. 72
  27. 24
  28. 36
  29. 34
  30. Yes
  31. 37
  32. 94
  33. 28
  34. 45
  35. Yes
  36. 34
  37. 45
  38. 77
  39. 71
  40. 18

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