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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 980 · 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 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)?
  2. 2.The angles of a triangle are in the ratio 3 : 3 : 4. What is the smallest angle (in degrees)?
  3. 3.In triangle ABC, angle A = 21° and angle B = 100°. What is angle C (in degrees)?
  4. 4.The two shorter sides of a right-angled triangle are 24 cm and 18 cm. How long is the longest side (in cm)?
  5. 5.The angles of a triangle are in the ratio 1 : 2 : 3. What is the biggest angle (in degrees)?
  6. 6.In a right-angled triangle, one of the other two angles is 44°. What is the third angle (in degrees)?
  7. 7.In triangle ABC, angle A = 68° and angle B = 38°. What is angle C (in degrees)?
  8. 8.In a right-angled triangle, one of the other two angles is 76°. What is the third angle (in degrees)?
  9. 9.Can a triangle have sides of 6 cm, 3 cm and 8 cm? (a) No (b) Yes
  10. 10.Can a triangle have sides of 11 cm, 6 cm and 6 cm? (a) Yes (b) No
  11. 11.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)?
  12. 12.The two interior opposite angles of a triangle are 22° and 38°. What is the exterior angle (in degrees)?
  13. 13.In a right-angled triangle, one of the other two angles is 49°. What is the third angle (in degrees)?
  14. 14.In triangle ABC, angle A = 25° and angle B = 45°. What is angle C (in degrees)?
  15. 15.An exterior angle of a triangle is 57°. One of its two interior opposite angles is 25°. What is the other one (in degrees)?
  16. 16.In triangle ABC, angle A = 95° and angle B = 25°. What is angle C (in degrees)?
  17. 17.An exterior angle of a triangle is 92°. One of its two interior opposite angles is 45°. What is the other one (in degrees)?
  18. 18.Can a triangle have sides of 4 cm, 8 cm and 14 cm? (a) Yes (b) No
  19. 19.In a right-angled triangle, one of the other two angles is 24°. What is the third angle (in degrees)?
  20. 20.In a right-angled triangle, one of the other two angles is 59°. What is the third angle (in degrees)?
  21. 21.In triangle ABC, angle A = 86° and angle B = 22°. What is angle C (in degrees)?
  22. 22.The two interior opposite angles of a triangle are 55° and 77°. What is the exterior angle (in degrees)?
  23. 23.The angles of a triangle are in the ratio 3 : 4 : 5. What is the biggest angle (in degrees)?
  24. 24.An exterior angle of a triangle is 79°. One of its two interior opposite angles is 56°. What is the other one (in degrees)?
  25. 25.In an isosceles triangle, the two equal angles are 44° each. What is the third angle (in degrees)?
  26. 26.In an isosceles triangle, the angle between the two equal sides is 58°. What is each of the other two angles (in degrees)?
  27. 27.The angles of a triangle are in the ratio 3 : 3 : 4. What is the biggest angle (in degrees)?
  28. 28.An exterior angle of a triangle is 124°. One of its two interior opposite angles is 44°. What is the other one (in degrees)?
  29. 29.In an isosceles triangle, the two equal angles are 38° each. What is the third angle (in degrees)?
  30. 30.In an isosceles triangle, the two equal angles are 48° each. What is the third angle (in degrees)?
  31. 31.The longest side of a right-angled triangle is 20 cm and one of the other sides is 12 cm. How long is the third side (in cm)?
  32. 32.The angles of a triangle are in the ratio 5 : 6 : 7. What is the biggest angle (in degrees)?
  33. 33.The two interior opposite angles of a triangle are 38° and 52°. What is the exterior angle (in degrees)?
  34. 34.The two interior opposite angles of a triangle are 51° and 74°. What is the exterior angle (in degrees)?
  35. 35.An exterior angle of a triangle is 99°. One of its two interior opposite angles is 58°. What is the other one (in degrees)?
  36. 36.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles (in degrees)?
  37. 37.In a right-angled triangle, one of the other two angles is 46°. What is the third angle (in degrees)?
  38. 38.Can a triangle have sides of 10 cm, 26 cm and 12 cm? (a) Yes (b) No
  39. 39.The two shorter sides of a right-angled triangle are 15 cm and 36 cm. How long is the longest side (in cm)?
  40. 40.The longest side of a right-angled triangle is 13 cm and one of the other sides is 5 cm. How long is the third side (in cm)?

Answer key

  1. 36
  2. 54
  3. 59
  4. 30
  5. 90
  6. 46
  7. 74
  8. 14
  9. Yes
  10. Yes
  11. 15
  12. 60
  13. 41
  14. 110
  15. 32
  16. 60
  17. 47
  18. No
  19. 66
  20. 31
  21. 72
  22. 132
  23. 75
  24. 23
  25. 92
  26. 61
  27. 72
  28. 80
  29. 104
  30. 84
  31. 16
  32. 70
  33. 90
  34. 125
  35. 41
  36. 20
  37. 44
  38. No
  39. 39
  40. 12

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