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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 454 · 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 10°. What is the third angle (in degrees)?
  2. 2.The two interior opposite angles of a triangle are 25° and 29°. What is the exterior angle (in degrees)?
  3. 3.The two interior opposite angles of a triangle are 53° and 79°. What is the exterior angle (in degrees)?
  4. 4.In a right-angled triangle, one of the other two angles is 58°. What is the third angle (in degrees)?
  5. 5.The longest side of a right-angled triangle is 26 cm and one of the other sides is 24 cm. How long is the third side (in cm)?
  6. 6.Can a triangle have sides of 3 cm, 3 cm and 2 cm? (a) No (b) Yes
  7. 7.The two interior opposite angles of a triangle are 46° and 55°. What is the exterior angle (in degrees)?
  8. 8.Can a triangle have sides of 12 cm, 10 cm and 6 cm? (a) Yes (b) No
  9. 9.The angles of a triangle are in the ratio 5 : 6 : 7. What is the smallest angle (in degrees)?
  10. 10.The angles of a triangle are in the ratio 2 : 3 : 4. What is the smallest angle (in degrees)?
  11. 11.An exterior angle of a triangle is 103°. One of its two interior opposite angles is 36°. What is the other one (in degrees)?
  12. 12.An exterior angle of a triangle is 118°. One of its two interior opposite angles is 42°. What is the other one (in degrees)?
  13. 13.An exterior angle of a triangle is 103°. One of its two interior opposite angles is 39°. What is the other one (in degrees)?
  14. 14.The angles of a triangle are in the ratio 3 : 5 : 7. What is the biggest angle (in degrees)?
  15. 15.In a right-angled triangle, one of the other two angles is 39°. What is the third angle (in degrees)?
  16. 16.Can a triangle have sides of 6 cm, 6 cm and 11 cm? (a) Yes (b) No
  17. 17.Can a triangle have sides of 10 cm, 3 cm and 11 cm? (a) Yes (b) No
  18. 18.In a right-angled triangle, one of the other two angles is 19°. What is the third angle (in degrees)?
  19. 19.In an isosceles triangle, the two equal angles are 72° each. What is the third angle (in degrees)?
  20. 20.Can a triangle have sides of 9 cm, 10 cm and 3 cm? (a) Yes (b) No
  21. 21.The longest side of a right-angled triangle is 5 cm and one of the other sides is 4 cm. How long is the third side (in cm)?
  22. 22.In an isosceles triangle, the angle between the two equal sides is 112°. What is each of the other two angles (in degrees)?
  23. 23.In a right-angled triangle, one of the other two angles is 51°. What is the third angle (in degrees)?
  24. 24.The longest side of a right-angled triangle is 26 cm and one of the other sides is 10 cm. How long is the third side (in cm)?
  25. 25.The two interior opposite angles of a triangle are 61° and 21°. What is the exterior angle (in degrees)?
  26. 26.An exterior angle of a triangle is 124°. One of its two interior opposite angles is 74°. What is the other one (in degrees)?
  27. 27.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)?
  28. 28.In a right-angled triangle, one of the other two angles is 64°. What is the third angle (in degrees)?
  29. 29.The two shorter sides of a right-angled triangle are 8 cm and 15 cm. How long is the longest side (in cm)?
  30. 30.An exterior angle of a triangle is 73°. One of its two interior opposite angles is 50°. What is the other one (in degrees)?
  31. 31.In triangle ABC, angle A = 66° and angle B = 52°. What is angle C (in degrees)?
  32. 32.The angles of a triangle are in the ratio 3 : 3 : 4. What is the smallest angle (in degrees)?
  33. 33.The two shorter sides of a right-angled triangle are 10 cm and 24 cm. How long is the longest side (in cm)?
  34. 34.Can a triangle have sides of 8 cm, 17 cm and 9 cm? (a) No (b) Yes
  35. 35.In triangle ABC, angle A = 32° and angle B = 116°. What is angle C (in degrees)?
  36. 36.The angles of a triangle are in the ratio 3 : 4 : 5. What is the biggest angle (in degrees)?
  37. 37.In triangle ABC, angle A = 45° and angle B = 33°. What is angle C (in degrees)?
  38. 38.An exterior angle of a triangle is 65°. One of its two interior opposite angles is 26°. What is the other one (in degrees)?
  39. 39.In triangle ABC, angle A = 78° and angle B = 53°. What is angle C (in degrees)?
  40. 40.An exterior angle of a triangle is 100°. One of its two interior opposite angles is 69°. What is the other one (in degrees)?

Answer key

  1. 80
  2. 54
  3. 132
  4. 32
  5. 10
  6. Yes
  7. 101
  8. Yes
  9. 50
  10. 40
  11. 67
  12. 76
  13. 64
  14. 84
  15. 51
  16. Yes
  17. Yes
  18. 71
  19. 36
  20. Yes
  21. 3
  22. 34
  23. 39
  24. 24
  25. 82
  26. 50
  27. 15
  28. 26
  29. 17
  30. 23
  31. 62
  32. 54
  33. 26
  34. No
  35. 32
  36. 75
  37. 102
  38. 39
  39. 49
  40. 31

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