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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 634 · 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.In a right-angled triangle, one of the other two angles is 78°. What is the third angle (in degrees)?
  2. 2.In a right-angled triangle, one of the other two angles is 53°. What is the third angle (in degrees)?
  3. 3.The angles of a triangle are in the ratio 2 : 3 : 5. What is the biggest angle (in degrees)?
  4. 4.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles (in degrees)?
  5. 5.The angles of a triangle are in the ratio 1 : 1 : 2. What is the smallest angle (in degrees)?
  6. 6.The two shorter sides of a right-angled triangle are 6 cm and 8 cm. How long is the longest side (in cm)?
  7. 7.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)?
  8. 8.An exterior angle of a triangle is 111°. One of its two interior opposite angles is 61°. What is the other one (in degrees)?
  9. 9.In triangle ABC, angle A = 36° and angle B = 103°. What is angle C (in degrees)?
  10. 10.In triangle ABC, angle A = 50° and angle B = 40°. What is angle C (in degrees)?
  11. 11.The angles of a triangle are in the ratio 1 : 2 : 6. What is the biggest angle (in degrees)?
  12. 12.Can a triangle have sides of 9 cm, 14 cm and 5 cm? (a) No (b) Yes
  13. 13.In triangle ABC, angle A = 82° and angle B = 35°. What is angle C (in degrees)?
  14. 14.The angles of a triangle are in the ratio 3 : 5 : 7. What is the smallest angle (in degrees)?
  15. 15.An exterior angle of a triangle is 125°. One of its two interior opposite angles is 54°. What is the other one (in degrees)?
  16. 16.In triangle ABC, angle A = 69° and angle B = 39°. What is angle C (in degrees)?
  17. 17.In triangle ABC, angle A = 20° and angle B = 120°. What is angle C (in degrees)?
  18. 18.In an isosceles triangle, the angle between the two equal sides is 24°. What is each of the other two angles (in degrees)?
  19. 19.The angles of a triangle are in the ratio 2 : 3 : 5. What is the smallest angle (in degrees)?
  20. 20.An exterior angle of a triangle is 151°. One of its two interior opposite angles is 72°. What is the other one (in degrees)?
  21. 21.Can a triangle have sides of 9 cm, 22 cm and 9 cm? (a) No (b) Yes
  22. 22.The angles of a triangle are in the ratio 2 : 3 : 4. What is the smallest angle (in degrees)?
  23. 23.The two shorter sides of a right-angled triangle are 24 cm and 10 cm. How long is the longest side (in cm)?
  24. 24.In triangle ABC, angle A = 44° and angle B = 90°. What is angle C (in degrees)?
  25. 25.In triangle ABC, angle A = 60° and angle B = 32°. What is angle C (in degrees)?
  26. 26.In triangle ABC, angle A = 61° and angle B = 74°. What is angle C (in degrees)?
  27. 27.Can a triangle have sides of 9 cm, 9 cm and 23 cm? (a) No (b) Yes
  28. 28.Can a triangle have sides of 9 cm, 3 cm and 9 cm? (a) No (b) Yes
  29. 29.The angles of a triangle are in the ratio 1 : 3 : 5. What is the smallest angle (in degrees)?
  30. 30.In triangle ABC, angle A = 63° and angle B = 74°. What is angle C (in degrees)?
  31. 31.In triangle ABC, angle A = 60° and angle B = 54°. What is angle C (in degrees)?
  32. 32.In triangle ABC, angle A = 93° and angle B = 35°. What is angle C (in degrees)?
  33. 33.The two shorter sides of a right-angled triangle are 5 cm and 12 cm. How long is the longest side (in cm)?
  34. 34.In a right-angled triangle, one of the other two angles is 27°. What is the third angle (in degrees)?
  35. 35.In an isosceles triangle, the angle between the two equal sides is 154°. What is each of the other two angles (in degrees)?
  36. 36.An exterior angle of a triangle is 93°. One of its two interior opposite angles is 43°. What is the other one (in degrees)?
  37. 37.The angles of a triangle are in the ratio 1 : 2 : 3. What is the smallest angle (in degrees)?
  38. 38.The angles of a triangle are in the ratio 2 : 2 : 5. What is the smallest angle (in degrees)?
  39. 39.An exterior angle of a triangle is 67°. One of its two interior opposite angles is 27°. What is the other one (in degrees)?
  40. 40.An exterior angle of a triangle is 68°. One of its two interior opposite angles is 24°. What is the other one (in degrees)?

Answer key

  1. 12
  2. 37
  3. 90
  4. 80
  5. 45
  6. 10
  7. 24
  8. 50
  9. 41
  10. 90
  11. 120
  12. No
  13. 63
  14. 36
  15. 71
  16. 72
  17. 40
  18. 78
  19. 36
  20. 79
  21. No
  22. 40
  23. 26
  24. 46
  25. 88
  26. 45
  27. No
  28. Yes
  29. 20
  30. 43
  31. 66
  32. 52
  33. 13
  34. 63
  35. 13
  36. 50
  37. 30
  38. 40
  39. 40
  40. 44

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