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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 257 · 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 two shorter sides of a right-angled triangle are 15 cm and 8 cm. How long is the longest side (in cm)?
  2. 2.The angles of a triangle are in the ratio 2 : 2 : 5. What is the smallest angle (in degrees)?
  3. 3.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles (in degrees)?
  4. 4.In triangle ABC, angle A = 73° and angle B = 22°. What is angle C (in degrees)?
  5. 5.The angles of a triangle are in the ratio 1 : 2 : 2. What is the smallest angle (in degrees)?
  6. 6.The two interior opposite angles of a triangle are 54° and 36°. What is the exterior angle (in degrees)?
  7. 7.In an isosceles triangle, the angle between the two equal sides is 126°. What is each of the other two angles (in degrees)?
  8. 8.In a right-angled triangle, one of the other two angles is 80°. What is the third angle (in degrees)?
  9. 9.The two interior opposite angles of a triangle are 75° and 29°. What is the exterior angle (in degrees)?
  10. 10.In a right-angled triangle, one of the other two angles is 13°. What is the third angle (in degrees)?
  11. 11.The two shorter sides of a right-angled triangle are 8 cm and 15 cm. How long is the longest side (in cm)?
  12. 12.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)?
  13. 13.In triangle ABC, angle A = 35° and angle B = 41°. What is angle C (in degrees)?
  14. 14.Can a triangle have sides of 6 cm, 9 cm and 7 cm? (a) No (b) Yes
  15. 15.The two interior opposite angles of a triangle are 62° and 29°. What is the exterior angle (in degrees)?
  16. 16.An exterior angle of a triangle is 84°. One of its two interior opposite angles is 53°. What is the other one (in degrees)?
  17. 17.In triangle ABC, angle A = 62° and angle B = 76°. What is angle C (in degrees)?
  18. 18.The two shorter sides of a right-angled triangle are 7 cm and 24 cm. How long is the longest side (in cm)?
  19. 19.In a right-angled triangle, one of the other two angles is 19°. What is the third angle (in degrees)?
  20. 20.The two interior opposite angles of a triangle are 36° and 47°. What is the exterior angle (in degrees)?
  21. 21.The angles of a triangle are in the ratio 1 : 2 : 2. What is the biggest angle (in degrees)?
  22. 22.Can a triangle have sides of 5 cm, 16 cm and 12 cm? (a) No (b) Yes
  23. 23.The two interior opposite angles of a triangle are 39° and 30°. What is the exterior angle (in degrees)?
  24. 24.An exterior angle of a triangle is 147°. One of its two interior opposite angles is 67°. What is the other one (in degrees)?
  25. 25.In a right-angled triangle, one of the other two angles is 15°. What is the third angle (in degrees)?
  26. 26.In triangle ABC, angle A = 56° and angle B = 66°. What is angle C (in degrees)?
  27. 27.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)?
  28. 28.An exterior angle of a triangle is 136°. One of its two interior opposite angles is 66°. What is the other one (in degrees)?
  29. 29.The angles of a triangle are in the ratio 4 : 5 : 6. What is the biggest angle (in degrees)?
  30. 30.The angles of a triangle are in the ratio 1 : 2 : 3. What is the biggest angle (in degrees)?
  31. 31.An exterior angle of a triangle is 96°. One of its two interior opposite angles is 73°. What is the other one (in degrees)?
  32. 32.The angles of a triangle are in the ratio 1 : 2 : 6. What is the biggest angle (in degrees)?
  33. 33.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles (in degrees)?
  34. 34.The two shorter sides of a right-angled triangle are 12 cm and 5 cm. How long is the longest side (in cm)?
  35. 35.In a right-angled triangle, one of the other two angles is 68°. What is the third angle (in degrees)?
  36. 36.The two interior opposite angles of a triangle are 80° and 62°. What is the exterior angle (in degrees)?
  37. 37.In an isosceles triangle, the two equal angles are 73° each. What is the third angle (in degrees)?
  38. 38.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)?
  39. 39.The two interior opposite angles of a triangle are 24° and 38°. What is the exterior angle (in degrees)?
  40. 40.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)?

Answer key

  1. 17
  2. 40
  3. 75
  4. 85
  5. 36
  6. 90
  7. 27
  8. 10
  9. 104
  10. 77
  11. 17
  12. 6
  13. 104
  14. Yes
  15. 91
  16. 31
  17. 42
  18. 25
  19. 71
  20. 83
  21. 72
  22. Yes
  23. 69
  24. 80
  25. 75
  26. 58
  27. 12
  28. 70
  29. 72
  30. 90
  31. 23
  32. 120
  33. 80
  34. 13
  35. 22
  36. 142
  37. 34
  38. 8
  39. 62
  40. 24

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