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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 411 · 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 triangle ABC, angle A = 25° and angle B = 42°. What is angle C (in degrees)?
  2. 2.The angles of a triangle are in the ratio 1 : 3 : 5. What is the smallest angle (in degrees)?
  3. 3.In triangle ABC, angle A = 36° and angle B = 31°. What is angle C (in degrees)?
  4. 4.The two shorter sides of a right-angled triangle are 36 cm and 15 cm. How long is the longest side (in cm)?
  5. 5.In an isosceles triangle, the angle between the two equal sides is 138°. What is each of the other two angles (in degrees)?
  6. 6.The two shorter sides of a right-angled triangle are 24 cm and 7 cm. How long is the longest side (in cm)?
  7. 7.Can a triangle have sides of 5 cm, 10 cm and 7 cm? (a) No (b) Yes
  8. 8.An exterior angle of a triangle is 94°. One of its two interior opposite angles is 54°. What is the other one (in degrees)?
  9. 9.In a right-angled triangle, one of the other two angles is 77°. What is the third angle (in degrees)?
  10. 10.The two shorter sides of a right-angled triangle are 8 cm and 15 cm. How long is the longest side (in cm)?
  11. 11.In triangle ABC, angle A = 39° and angle B = 92°. What is angle C (in degrees)?
  12. 12.In an isosceles triangle, the angle between the two equal sides is 52°. What is each of the other two angles (in degrees)?
  13. 13.In triangle ABC, angle A = 90° and angle B = 41°. What is angle C (in degrees)?
  14. 14.Can a triangle have sides of 10 cm, 2 cm and 12 cm? (a) Yes (b) No
  15. 15.Can a triangle have sides of 11 cm, 2 cm and 12 cm? (a) Yes (b) No
  16. 16.The angles of a triangle are in the ratio 2 : 7 : 9. What is the smallest angle (in degrees)?
  17. 17.The two shorter sides of a right-angled triangle are 24 cm and 18 cm. How long is the longest side (in cm)?
  18. 18.In a right-angled triangle, one of the other two angles is 27°. What is the third angle (in degrees)?
  19. 19.An exterior angle of a triangle is 143°. One of its two interior opposite angles is 77°. What is the other one (in degrees)?
  20. 20.In an isosceles triangle, the angle between the two equal sides is 58°. What is each of the other two angles (in degrees)?
  21. 21.The two interior opposite angles of a triangle are 46° and 61°. What is the exterior angle (in degrees)?
  22. 22.In a right-angled triangle, one of the other two angles is 13°. What is the third angle (in degrees)?
  23. 23.In triangle ABC, angle A = 58° and angle B = 25°. What is angle C (in degrees)?
  24. 24.The angles of a triangle are in the ratio 1 : 2 : 3. What is the biggest angle (in degrees)?
  25. 25.The longest side of a right-angled triangle is 10 cm and one of the other sides is 6 cm. How long is the third side (in cm)?
  26. 26.In triangle ABC, angle A = 77° and angle B = 72°. What is angle C (in degrees)?
  27. 27.The longest side of a right-angled triangle is 30 cm and one of the other sides is 24 cm. How long is the third side (in cm)?
  28. 28.The longest side of a right-angled triangle is 39 cm and one of the other sides is 36 cm. How long is the third side (in cm)?
  29. 29.Can a triangle have sides of 2 cm, 5 cm and 11 cm? (a) Yes (b) No
  30. 30.Can a triangle have sides of 9 cm, 8 cm and 2 cm? (a) No (b) Yes
  31. 31.The angles of a triangle are in the ratio 3 : 4 : 5. What is the smallest angle (in degrees)?
  32. 32.The longest side of a right-angled triangle is 39 cm and one of the other sides is 15 cm. How long is the third side (in cm)?
  33. 33.An exterior angle of a triangle is 81°. One of its two interior opposite angles is 61°. What is the other one (in degrees)?
  34. 34.An exterior angle of a triangle is 97°. One of its two interior opposite angles is 24°. What is the other one (in degrees)?
  35. 35.In triangle ABC, angle A = 76° and angle B = 41°. What is angle C (in degrees)?
  36. 36.In triangle ABC, angle A = 54° and angle B = 102°. What is angle C (in degrees)?
  37. 37.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)?
  38. 38.In triangle ABC, angle A = 22° and angle B = 120°. What is angle C (in degrees)?
  39. 39.In an isosceles triangle, the angle between the two equal sides is 32°. What is each of the other two angles (in degrees)?
  40. 40.In triangle ABC, angle A = 78° and angle B = 52°. What is angle C (in degrees)?

Answer key

  1. 113
  2. 20
  3. 113
  4. 39
  5. 21
  6. 25
  7. Yes
  8. 40
  9. 13
  10. 17
  11. 49
  12. 64
  13. 49
  14. No
  15. Yes
  16. 20
  17. 30
  18. 63
  19. 66
  20. 61
  21. 107
  22. 77
  23. 97
  24. 90
  25. 8
  26. 31
  27. 18
  28. 15
  29. No
  30. Yes
  31. 45
  32. 36
  33. 20
  34. 73
  35. 63
  36. 24
  37. 15
  38. 38
  39. 74
  40. 50

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