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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 628 · 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 64°. What is the third angle (in degrees)?
  2. 2.In triangle ABC, angle A = 39° and angle B = 38°. What is angle C (in degrees)?
  3. 3.In triangle ABC, angle A = 23° and angle B = 97°. What is angle C (in degrees)?
  4. 4.The two shorter sides of a right-angled triangle are 12 cm and 9 cm. How long is the longest side (in cm)?
  5. 5.An exterior angle of a triangle is 100°. One of its two interior opposite angles is 53°. What is the other one (in degrees)?
  6. 6.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)?
  7. 7.Can a triangle have sides of 6 cm, 5 cm and 6 cm? (a) No (b) Yes
  8. 8.The two shorter sides of a right-angled triangle are 8 cm and 15 cm. How long is the longest side (in cm)?
  9. 9.The two interior opposite angles of a triangle are 58° and 59°. What is the exterior angle (in degrees)?
  10. 10.In an isosceles triangle, the angle between the two equal sides is 116°. What is each of the other two angles (in degrees)?
  11. 11.An exterior angle of a triangle is 109°. One of its two interior opposite angles is 77°. What is the other one (in degrees)?
  12. 12.In triangle ABC, angle A = 84° and angle B = 27°. What is angle C (in degrees)?
  13. 13.In triangle ABC, angle A = 70° and angle B = 37°. What is angle C (in degrees)?
  14. 14.The two interior opposite angles of a triangle are 25° and 33°. What is the exterior angle (in degrees)?
  15. 15.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)?
  16. 16.In an isosceles triangle, the angle between the two equal sides is 128°. What is each of the other two angles (in degrees)?
  17. 17.Can a triangle have sides of 8 cm, 14 cm and 4 cm? (a) Yes (b) No
  18. 18.In an isosceles triangle, the two equal angles are 76° each. What is the third angle (in degrees)?
  19. 19.In triangle ABC, angle A = 77° and angle B = 24°. What is angle C (in degrees)?
  20. 20.The two interior opposite angles of a triangle are 29° and 40°. What is the exterior angle (in degrees)?
  21. 21.Can a triangle have sides of 7 cm, 19 cm and 7 cm? (a) Yes (b) No
  22. 22.In an isosceles triangle, the angle between the two equal sides is 104°. What is each of the other two angles (in degrees)?
  23. 23.Can a triangle have sides of 7 cm, 12 cm and 21 cm? (a) Yes (b) No
  24. 24.The angles of a triangle are in the ratio 3 : 4 : 5. What is the smallest angle (in degrees)?
  25. 25.An exterior angle of a triangle is 97°. One of its two interior opposite angles is 77°. What is the other one (in degrees)?
  26. 26.In an isosceles triangle, the angle between the two equal sides is 24°. What is each of the other two angles (in degrees)?
  27. 27.The longest side of a right-angled triangle is 10 cm and one of the other sides is 6 cm. How long is the third side (in cm)?
  28. 28.In an isosceles triangle, the two equal angles are 26° each. What is the third angle (in degrees)?
  29. 29.In a right-angled triangle, one of the other two angles is 59°. What is the third angle (in degrees)?
  30. 30.In a right-angled triangle, one of the other two angles is 38°. What is the third angle (in degrees)?
  31. 31.Can a triangle have sides of 2 cm, 3 cm and 4 cm? (a) Yes (b) No
  32. 32.The angles of a triangle are in the ratio 3 : 3 : 4. What is the smallest angle (in degrees)?
  33. 33.In a right-angled triangle, one of the other two angles is 77°. What is the third angle (in degrees)?
  34. 34.In a right-angled triangle, one of the other two angles is 62°. What is the third angle (in degrees)?
  35. 35.The angles of a triangle are in the ratio 1 : 3 : 5. What is the smallest angle (in degrees)?
  36. 36.The two shorter sides of a right-angled triangle are 7 cm and 24 cm. How long is the longest side (in cm)?
  37. 37.Can a triangle have sides of 11 cm, 7 cm and 18 cm? (a) No (b) Yes
  38. 38.The angles of a triangle are in the ratio 4 : 5 : 6. What is the biggest angle (in degrees)?
  39. 39.In an isosceles triangle, the angle between the two equal sides is 96°. What is each of the other two angles (in degrees)?
  40. 40.In triangle ABC, angle A = 52° and angle B = 46°. What is angle C (in degrees)?

Answer key

  1. 26
  2. 103
  3. 60
  4. 15
  5. 47
  6. 7
  7. Yes
  8. 17
  9. 117
  10. 32
  11. 32
  12. 69
  13. 73
  14. 58
  15. 24
  16. 26
  17. No
  18. 28
  19. 79
  20. 69
  21. No
  22. 38
  23. No
  24. 45
  25. 20
  26. 78
  27. 8
  28. 128
  29. 31
  30. 52
  31. Yes
  32. 54
  33. 13
  34. 28
  35. 20
  36. 25
  37. No
  38. 72
  39. 42
  40. 82

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