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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 945 · 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 an isosceles triangle, the angle between the two equal sides is 102°. What is each of the other two angles (in degrees)?
  2. 2.In a right-angled triangle, one of the other two angles is 21°. What is the third angle (in degrees)?
  3. 3.In an isosceles triangle, the angle between the two equal sides is 158°. What is each of the other two angles (in degrees)?
  4. 4.In a right-angled triangle, one of the other two angles is 31°. What is the third angle (in degrees)?
  5. 5.In triangle ABC, angle A = 51° and angle B = 22°. What is angle C (in degrees)?
  6. 6.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)?
  7. 7.In a right-angled triangle, one of the other two angles is 40°. What is the third angle (in degrees)?
  8. 8.Can a triangle have sides of 5 cm, 8 cm and 4 cm? (a) No (b) Yes
  9. 9.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)?
  10. 10.An exterior angle of a triangle is 75°. One of its two interior opposite angles is 38°. What is the other one (in degrees)?
  11. 11.In a right-angled triangle, one of the other two angles is 55°. What is the third angle (in degrees)?
  12. 12.The two shorter sides of a right-angled triangle are 15 cm and 8 cm. How long is the longest side (in cm)?
  13. 13.In triangle ABC, angle A = 62° and angle B = 94°. What is angle C (in degrees)?
  14. 14.Can a triangle have sides of 2 cm, 9 cm and 6 cm? (a) Yes (b) No
  15. 15.The longest side of a right-angled triangle is 25 cm and one of the other sides is 24 cm. How long is the third side (in cm)?
  16. 16.In triangle ABC, angle A = 45° and angle B = 101°. What is angle C (in degrees)?
  17. 17.An exterior angle of a triangle is 121°. One of its two interior opposite angles is 52°. What is the other one (in degrees)?
  18. 18.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)?
  19. 19.The angles of a triangle are in the ratio 1 : 2 : 2. What is the smallest angle (in degrees)?
  20. 20.The two shorter sides of a right-angled triangle are 7 cm and 24 cm. How long is the longest side (in cm)?
  21. 21.In a right-angled triangle, one of the other two angles is 13°. What is the third angle (in degrees)?
  22. 22.In an isosceles triangle, the angle between the two equal sides is 126°. What is each of the other two angles (in degrees)?
  23. 23.The two interior opposite angles of a triangle are 20° and 33°. What is the exterior angle (in degrees)?
  24. 24.Can a triangle have sides of 9 cm, 11 cm and 5 cm? (a) No (b) Yes
  25. 25.The two shorter sides of a right-angled triangle are 10 cm and 24 cm. How long is the longest side (in cm)?
  26. 26.The angles of a triangle are in the ratio 3 : 4 : 5. What is the biggest angle (in degrees)?
  27. 27.In a right-angled triangle, one of the other two angles is 29°. What is the third angle (in degrees)?
  28. 28.In an isosceles triangle, the angle between the two equal sides is 106°. 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.In an isosceles triangle, the angle between the two equal sides is 98°. What is each of the other two angles (in degrees)?
  31. 31.Can a triangle have sides of 9 cm, 3 cm and 7 cm? (a) Yes (b) No
  32. 32.In triangle ABC, angle A = 40° and angle B = 27°. What is angle C (in degrees)?
  33. 33.In triangle ABC, angle A = 28° and angle B = 112°. What is angle C (in degrees)?
  34. 34.The angles of a triangle are in the ratio 5 : 6 : 7. What is the biggest angle (in degrees)?
  35. 35.In triangle ABC, angle A = 84° and angle B = 69°. What is angle C (in degrees)?
  36. 36.In triangle ABC, angle A = 92° and angle B = 32°. What is angle C (in degrees)?
  37. 37.In a right-angled triangle, one of the other two angles is 75°. What is the third angle (in degrees)?
  38. 38.Can a triangle have sides of 7 cm, 9 cm and 16 cm? (a) No (b) Yes
  39. 39.An exterior angle of a triangle is 132°. One of its two interior opposite angles is 55°. What is the other one (in degrees)?
  40. 40.In an isosceles triangle, the two equal angles are 80° each. What is the third angle (in degrees)?

Answer key

  1. 39
  2. 69
  3. 11
  4. 59
  5. 107
  6. 24
  7. 50
  8. Yes
  9. 15
  10. 37
  11. 35
  12. 17
  13. 24
  14. No
  15. 7
  16. 34
  17. 69
  18. 18
  19. 36
  20. 25
  21. 77
  22. 27
  23. 53
  24. Yes
  25. 26
  26. 75
  27. 61
  28. 37
  29. 34
  30. 41
  31. Yes
  32. 113
  33. 40
  34. 70
  35. 27
  36. 56
  37. 15
  38. No
  39. 77
  40. 20

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