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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 279 · 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 a right-angled triangle, one of the other two angles is 69°. What is the third angle (in degrees)?
  2. 2.In an isosceles triangle, the two equal angles are 72° each. What is the third angle (in degrees)?
  3. 3.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)?
  4. 4.The angles of a triangle are in the ratio 1 : 2 : 3. What is the biggest angle (in degrees)?
  5. 5.In triangle ABC, angle A = 47° and angle B = 63°. What is angle C (in degrees)?
  6. 6.Can a triangle have sides of 3 cm, 4 cm and 4 cm? (a) Yes (b) No
  7. 7.In a right-angled triangle, one of the other two angles is 21°. What is the third angle (in degrees)?
  8. 8.In triangle ABC, angle A = 60° and angle B = 89°. What is angle C (in degrees)?
  9. 9.An exterior angle of a triangle is 51°. One of its two interior opposite angles is 20°. What is the other one (in degrees)?
  10. 10.In triangle ABC, angle A = 47° and angle B = 104°. What is angle C (in degrees)?
  11. 11.In triangle ABC, angle A = 99° and angle B = 53°. What is angle C (in degrees)?
  12. 12.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)?
  13. 13.The angles of a triangle are in the ratio 1 : 4 : 5. What is the smallest angle (in degrees)?
  14. 14.Can a triangle have sides of 2 cm, 4 cm and 4 cm? (a) Yes (b) No
  15. 15.The angles of a triangle are in the ratio 1 : 2 : 6. What is the smallest angle (in degrees)?
  16. 16.The two shorter sides of a right-angled triangle are 10 cm and 24 cm. How long is the longest side (in cm)?
  17. 17.In triangle ABC, angle A = 30° and angle B = 27°. What is angle C (in degrees)?
  18. 18.Can a triangle have sides of 20 cm, 12 cm and 8 cm? (a) Yes (b) No
  19. 19.In triangle ABC, angle A = 35° and angle B = 116°. What is angle C (in degrees)?
  20. 20.In an isosceles triangle, the angle between the two equal sides is 42°. What is each of the other two angles (in degrees)?
  21. 21.In triangle ABC, angle A = 79° and angle B = 41°. What is angle C (in degrees)?
  22. 22.In an isosceles triangle, the angle between the two equal sides is 22°. What is each of the other two angles (in degrees)?
  23. 23.An exterior angle of a triangle is 155°. One of its two interior opposite angles is 77°. What is the other one (in degrees)?
  24. 24.The angles of a triangle are in the ratio 1 : 3 : 5. What is the smallest angle (in degrees)?
  25. 25.The two shorter sides of a right-angled triangle are 24 cm and 7 cm. How long is the longest side (in cm)?
  26. 26.In a right-angled triangle, one of the other two angles is 11°. What is the third angle (in degrees)?
  27. 27.An exterior angle of a triangle is 77°. One of its two interior opposite angles is 48°. What is the other one (in degrees)?
  28. 28.An exterior angle of a triangle is 82°. One of its two interior opposite angles is 30°. What is the other one (in degrees)?
  29. 29.The angles of a triangle are in the ratio 3 : 3 : 4. What is the smallest angle (in degrees)?
  30. 30.In a right-angled triangle, one of the other two angles is 56°. What is the third angle (in degrees)?
  31. 31.The angles of a triangle are in the ratio 3 : 5 : 7. What is the biggest angle (in degrees)?
  32. 32.In a right-angled triangle, one of the other two angles is 50°. What is the third angle (in degrees)?
  33. 33.An exterior angle of a triangle is 84°. One of its two interior opposite angles is 58°. What is the other one (in degrees)?
  34. 34.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles (in degrees)?
  35. 35.In triangle ABC, angle A = 76° and angle B = 43°. What is angle C (in degrees)?
  36. 36.The angles of a triangle are in the ratio 4 : 5 : 6. What is the smallest angle (in degrees)?
  37. 37.In triangle ABC, angle A = 72° and angle B = 77°. What is angle C (in degrees)?
  38. 38.In a right-angled triangle, one of the other two angles is 29°. What is the third angle (in degrees)?
  39. 39.The longest side of a right-angled triangle is 25 cm and one of the other sides is 15 cm. How long is the third side (in cm)?
  40. 40.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)?

Answer key

  1. 21
  2. 36
  3. 12
  4. 90
  5. 70
  6. Yes
  7. 69
  8. 31
  9. 31
  10. 29
  11. 28
  12. 7
  13. 18
  14. Yes
  15. 20
  16. 26
  17. 123
  18. No
  19. 29
  20. 69
  21. 60
  22. 79
  23. 78
  24. 20
  25. 25
  26. 79
  27. 29
  28. 52
  29. 54
  30. 34
  31. 84
  32. 40
  33. 26
  34. 50
  35. 61
  36. 48
  37. 31
  38. 61
  39. 20
  40. 15

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