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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 812 · 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 an isosceles triangle, the angle between the two equal sides is 152°. What is each of the other two angles (in degrees)?
  2. 2.An exterior angle of a triangle is 107°. One of its two interior opposite angles is 28°. What is the other one (in degrees)?
  3. 3.In a right-angled triangle, one of the other two angles is 21°. What is the third angle (in degrees)?
  4. 4.The two interior opposite angles of a triangle are 49° and 72°. What is the exterior angle (in degrees)?
  5. 5.The angles of a triangle are in the ratio 2 : 3 : 4. What is the biggest angle (in degrees)?
  6. 6.In an isosceles triangle, the angle between the two equal sides is 24°. What is each of the other two angles (in degrees)?
  7. 7.The two shorter sides of a right-angled triangle are 7 cm and 24 cm. How long is the longest side (in cm)?
  8. 8.In triangle ABC, angle A = 95° and angle B = 48°. What is angle C (in degrees)?
  9. 9.The angles of a triangle are in the ratio 1 : 2 : 2. What is the biggest angle (in degrees)?
  10. 10.In triangle ABC, angle A = 29° and angle B = 76°. What is angle C (in degrees)?
  11. 11.The longest side of a right-angled triangle is 15 cm and one of the other sides is 9 cm. How long is the third side (in cm)?
  12. 12.In a right-angled triangle, one of the other two angles is 79°. What is the third angle (in degrees)?
  13. 13.In triangle ABC, angle A = 35° and angle B = 61°. What is angle C (in degrees)?
  14. 14.The angles of a triangle are in the ratio 1 : 2 : 3. What is the smallest angle (in degrees)?
  15. 15.The two interior opposite angles of a triangle are 35° and 31°. What is the exterior angle (in degrees)?
  16. 16.The two interior opposite angles of a triangle are 60° and 45°. What is the exterior angle (in degrees)?
  17. 17.The two interior opposite angles of a triangle are 75° and 49°. What is the exterior angle (in degrees)?
  18. 18.The longest side of a right-angled triangle is 5 cm and one of the other sides is 3 cm. How long is the third side (in cm)?
  19. 19.An exterior angle of a triangle is 102°. One of its two interior opposite angles is 37°. What is the other one (in degrees)?
  20. 20.Can a triangle have sides of 3 cm, 2 cm and 4 cm? (a) No (b) Yes
  21. 21.Can a triangle have sides of 5 cm, 12 cm and 8 cm? (a) Yes (b) No
  22. 22.In an isosceles triangle, the angle between the two equal sides is 64°. What is each of the other two angles (in degrees)?
  23. 23.In triangle ABC, angle A = 31° and angle B = 71°. What is angle C (in degrees)?
  24. 24.Can a triangle have sides of 4 cm, 9 cm and 12 cm? (a) No (b) Yes
  25. 25.The angles of a triangle are in the ratio 1 : 3 : 5. What is the biggest angle (in degrees)?
  26. 26.In a right-angled triangle, one of the other two angles is 69°. What is the third angle (in degrees)?
  27. 27.The two shorter sides of a right-angled triangle are 6 cm and 8 cm. How long is the longest side (in cm)?
  28. 28.In triangle ABC, angle A = 70° and angle B = 67°. What is angle C (in degrees)?
  29. 29.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)?
  30. 30.In an isosceles triangle, the two equal angles are 62° each. What is the third angle (in degrees)?
  31. 31.The angles of a triangle are in the ratio 1 : 2 : 3. What is the biggest angle (in degrees)?
  32. 32.Can a triangle have sides of 2 cm, 4 cm and 3 cm? (a) No (b) Yes
  33. 33.An exterior angle of a triangle is 144°. One of its two interior opposite angles is 75°. What is the other one (in degrees)?
  34. 34.In an isosceles triangle, the two equal angles are 77° each. What is the third angle (in degrees)?
  35. 35.In triangle ABC, angle A = 20° and angle B = 113°. What is angle C (in degrees)?
  36. 36.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles (in degrees)?
  37. 37.In a right-angled triangle, one of the other two angles is 12°. What is the third angle (in degrees)?
  38. 38.An exterior angle of a triangle is 130°. One of its two interior opposite angles is 80°. What is the other one (in degrees)?
  39. 39.An exterior angle of a triangle is 102°. One of its two interior opposite angles is 54°. What is the other one (in degrees)?
  40. 40.In triangle ABC, angle A = 25° and angle B = 106°. What is angle C (in degrees)?

Answer key

  1. 14
  2. 79
  3. 69
  4. 121
  5. 80
  6. 78
  7. 25
  8. 37
  9. 72
  10. 75
  11. 12
  12. 11
  13. 84
  14. 30
  15. 66
  16. 105
  17. 124
  18. 4
  19. 65
  20. Yes
  21. Yes
  22. 58
  23. 78
  24. Yes
  25. 100
  26. 21
  27. 10
  28. 43
  29. 15
  30. 56
  31. 90
  32. Yes
  33. 69
  34. 26
  35. 47
  36. 70
  37. 78
  38. 50
  39. 48
  40. 49

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