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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 195 · 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 1 : 1 : 2. What is the smallest angle (in degrees)?
  2. 2.The longest side of a right-angled triangle is 25 cm and one of the other sides is 7 cm. How long is the third side (in cm)?
  3. 3.Can a triangle have sides of 3 cm, 3 cm and 3 cm? (a) No (b) Yes
  4. 4.In a right-angled triangle, one of the other two angles is 56°. What is the third angle (in degrees)?
  5. 5.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)?
  6. 6.Can a triangle have sides of 5 cm, 10 cm and 5 cm? (a) Yes (b) No
  7. 7.In a right-angled triangle, one of the other two angles is 70°. What is the third angle (in degrees)?
  8. 8.In an isosceles triangle, the angle between the two equal sides is 132°. What is each of the other two angles (in degrees)?
  9. 9.In an isosceles triangle, the two equal angles are 48° each. What is the third angle (in degrees)?
  10. 10.In an isosceles triangle, the two equal angles are 27° each. What is the third angle (in degrees)?
  11. 11.An exterior angle of a triangle is 111°. One of its two interior opposite angles is 50°. What is the other one (in degrees)?
  12. 12.In triangle ABC, angle A = 38° and angle B = 117°. What is angle C (in degrees)?
  13. 13.In triangle ABC, angle A = 43° and angle B = 27°. What is angle C (in degrees)?
  14. 14.In a right-angled triangle, one of the other two angles is 65°. What is the third angle (in degrees)?
  15. 15.In an isosceles triangle, the two equal angles are 52° each. What is the third angle (in degrees)?
  16. 16.Can a triangle have sides of 11 cm, 14 cm and 3 cm? (a) Yes (b) No
  17. 17.In a right-angled triangle, one of the other two angles is 50°. What is the third angle (in degrees)?
  18. 18.The angles of a triangle are in the ratio 1 : 2 : 2. What is the smallest angle (in degrees)?
  19. 19.In triangle ABC, angle A = 64° and angle B = 75°. What is angle C (in degrees)?
  20. 20.In triangle ABC, angle A = 88° and angle B = 62°. What is angle C (in degrees)?
  21. 21.In an isosceles triangle, the two equal angles are 41° each. What is the third angle (in degrees)?
  22. 22.Can a triangle have sides of 12 cm, 19 cm and 5 cm? (a) No (b) Yes
  23. 23.In triangle ABC, angle A = 66° and angle B = 32°. What is angle C (in degrees)?
  24. 24.In an isosceles triangle, the angle between the two equal sides is 72°. What is each of the other two angles (in degrees)?
  25. 25.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)?
  26. 26.The angles of a triangle are in the ratio 1 : 2 : 6. What is the biggest angle (in degrees)?
  27. 27.Can a triangle have sides of 9 cm, 10 cm and 3 cm? (a) No (b) Yes
  28. 28.In an isosceles triangle, the angle between the two equal sides is 56°. What is each of the other two angles (in degrees)?
  29. 29.An exterior angle of a triangle is 95°. One of its two interior opposite angles is 24°. What is the other one (in degrees)?
  30. 30.In triangle ABC, angle A = 43° and angle B = 24°. What is angle C (in degrees)?
  31. 31.An exterior angle of a triangle is 95°. One of its two interior opposite angles is 34°. What is the other one (in degrees)?
  32. 32.The two interior opposite angles of a triangle are 28° and 36°. What is the exterior angle (in degrees)?
  33. 33.In triangle ABC, angle A = 98° and angle B = 52°. What is angle C (in degrees)?
  34. 34.An exterior angle of a triangle is 112°. One of its two interior opposite angles is 77°. What is the other one (in degrees)?
  35. 35.Can a triangle have sides of 6 cm, 15 cm and 5 cm? (a) Yes (b) No
  36. 36.An exterior angle of a triangle is 74°. One of its two interior opposite angles is 25°. What is the other one (in degrees)?
  37. 37.An exterior angle of a triangle is 79°. One of its two interior opposite angles is 22°. What is the other one (in degrees)?
  38. 38.An exterior angle of a triangle is 98°. One of its two interior opposite angles is 75°. What is the other one (in degrees)?
  39. 39.In a right-angled triangle, one of the other two angles is 53°. What is the third angle (in degrees)?
  40. 40.The two shorter sides of a right-angled triangle are 12 cm and 9 cm. How long is the longest side (in cm)?

Answer key

  1. 45
  2. 24
  3. Yes
  4. 34
  5. 6
  6. No
  7. 20
  8. 24
  9. 84
  10. 126
  11. 61
  12. 25
  13. 110
  14. 25
  15. 76
  16. No
  17. 40
  18. 36
  19. 41
  20. 30
  21. 98
  22. No
  23. 82
  24. 54
  25. 12
  26. 120
  27. Yes
  28. 62
  29. 71
  30. 113
  31. 61
  32. 64
  33. 30
  34. 35
  35. No
  36. 49
  37. 57
  38. 23
  39. 37
  40. 15

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