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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 572 · 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.The angles of a triangle are in the ratio 3 : 3 : 4. What is the smallest angle (in degrees)?
  2. 2.In an isosceles triangle, the angle between the two equal sides is 78°. What is each of the other two angles (in degrees)?
  3. 3.The two shorter sides of a right-angled triangle are 8 cm and 15 cm. How long is the longest side (in cm)?
  4. 4.Can a triangle have sides of 18 cm, 7 cm and 6 cm? (a) Yes (b) No
  5. 5.Can a triangle have sides of 4 cm, 7 cm and 8 cm? (a) Yes (b) No
  6. 6.In a right-angled triangle, one of the other two angles is 34°. What is the third angle (in degrees)?
  7. 7.The angles of a triangle are in the ratio 1 : 1 : 2. What is the biggest angle (in degrees)?
  8. 8.The two shorter sides of a right-angled triangle are 15 cm and 8 cm. How long is the longest side (in cm)?
  9. 9.In triangle ABC, angle A = 29° and angle B = 77°. What is angle C (in degrees)?
  10. 10.In triangle ABC, angle A = 72° and angle B = 47°. What is angle C (in degrees)?
  11. 11.Can a triangle have sides of 10 cm, 7 cm and 6 cm? (a) No (b) Yes
  12. 12.In an isosceles triangle, the angle between the two equal sides is 28°. What is each of the other two angles (in degrees)?
  13. 13.The longest side of a right-angled triangle is 17 cm and one of the other sides is 15 cm. How long is the third side (in cm)?
  14. 14.In triangle ABC, angle A = 78° and angle B = 29°. What is angle C (in degrees)?
  15. 15.In a right-angled triangle, one of the other two angles is 70°. What is the third angle (in degrees)?
  16. 16.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)?
  17. 17.In a right-angled triangle, one of the other two angles is 23°. What is the third angle (in degrees)?
  18. 18.The two interior opposite angles of a triangle are 51° and 26°. What is the exterior angle (in degrees)?
  19. 19.In a right-angled triangle, one of the other two angles is 55°. What is the third angle (in degrees)?
  20. 20.The longest side of a right-angled triangle is 20 cm and one of the other sides is 16 cm. How long is the third side (in cm)?
  21. 21.Can a triangle have sides of 5 cm, 7 cm and 8 cm? (a) No (b) Yes
  22. 22.The two interior opposite angles of a triangle are 41° and 62°. What is the exterior angle (in degrees)?
  23. 23.In triangle ABC, angle A = 55° and angle B = 63°. What is angle C (in degrees)?
  24. 24.The two interior opposite angles of a triangle are 33° and 47°. What is the exterior angle (in degrees)?
  25. 25.The angles of a triangle are in the ratio 1 : 2 : 2. What is the smallest angle (in degrees)?
  26. 26.The longest side of a right-angled triangle is 10 cm and one of the other sides is 8 cm. How long is the third side (in cm)?
  27. 27.In a right-angled triangle, one of the other two angles is 30°. What is the third angle (in degrees)?
  28. 28.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)?
  29. 29.In a right-angled triangle, one of the other two angles is 59°. What is the third angle (in degrees)?
  30. 30.In triangle ABC, angle A = 26° and angle B = 97°. What is angle C (in degrees)?
  31. 31.In an isosceles triangle, the angle between the two equal sides is 66°. What is each of the other two angles (in degrees)?
  32. 32.The two interior opposite angles of a triangle are 55° and 70°. What is the exterior angle (in degrees)?
  33. 33.Can a triangle have sides of 12 cm, 8 cm and 7 cm? (a) No (b) Yes
  34. 34.In a right-angled triangle, one of the other two angles is 19°. What is the third angle (in degrees)?
  35. 35.In an isosceles triangle, the angle between the two equal sides is 128°. What is each of the other two angles (in degrees)?
  36. 36.Can a triangle have sides of 11 cm, 10 cm and 6 cm? (a) No (b) Yes
  37. 37.An exterior angle of a triangle is 109°. One of its two interior opposite angles is 78°. What is the other one (in degrees)?
  38. 38.The angles of a triangle are in the ratio 2 : 3 : 4. What is the smallest angle (in degrees)?
  39. 39.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)?
  40. 40.Can a triangle have sides of 6 cm, 9 cm and 5 cm? (a) Yes (b) No

Answer key

  1. 54
  2. 51
  3. 17
  4. No
  5. Yes
  6. 56
  7. 90
  8. 17
  9. 74
  10. 61
  11. Yes
  12. 76
  13. 8
  14. 73
  15. 20
  16. 8
  17. 67
  18. 77
  19. 35
  20. 12
  21. Yes
  22. 103
  23. 62
  24. 80
  25. 36
  26. 6
  27. 60
  28. 7
  29. 31
  30. 57
  31. 57
  32. 125
  33. Yes
  34. 71
  35. 26
  36. Yes
  37. 31
  38. 40
  39. 24
  40. Yes

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