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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 818 · 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 3 : 3 : 4. What is the smallest angle (in degrees)?
  3. 3.In an isosceles triangle, the angle between the two equal sides is 32°. What is each of the other two angles (in degrees)?
  4. 4.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles (in degrees)?
  5. 5.In a right-angled triangle, one of the other two angles is 18°. What is the third angle (in degrees)?
  6. 6.The two interior opposite angles of a triangle are 27° and 77°. What is the exterior angle (in degrees)?
  7. 7.The angles of a triangle are in the ratio 1 : 2 : 2. What is the smallest angle (in degrees)?
  8. 8.An exterior angle of a triangle is 79°. One of its two interior opposite angles is 47°. What is the other one (in degrees)?
  9. 9.The two shorter sides of a right-angled triangle are 5 cm and 12 cm. How long is the longest side (in cm)?
  10. 10.Can a triangle have sides of 5 cm, 3 cm and 4 cm? (a) Yes (b) No
  11. 11.Can a triangle have sides of 7 cm, 11 cm and 23 cm? (a) Yes (b) No
  12. 12.Can a triangle have sides of 6 cm, 10 cm and 18 cm? (a) No (b) Yes
  13. 13.In triangle ABC, angle A = 28° and angle B = 76°. What is angle C (in degrees)?
  14. 14.In an isosceles triangle, the angle between the two equal sides is 146°. What is each of the other two angles (in degrees)?
  15. 15.The two shorter sides of a right-angled triangle are 12 cm and 9 cm. How long is the longest side (in cm)?
  16. 16.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles (in degrees)?
  17. 17.In an isosceles triangle, the angle between the two equal sides is 28°. What is each of the other two angles (in degrees)?
  18. 18.The two interior opposite angles of a triangle are 70° and 33°. What is the exterior angle (in degrees)?
  19. 19.In triangle ABC, angle A = 96° and angle B = 36°. What is angle C (in degrees)?
  20. 20.In triangle ABC, angle A = 45° and angle B = 87°. What is angle C (in degrees)?
  21. 21.The two interior opposite angles of a triangle are 46° and 57°. What is the exterior angle (in degrees)?
  22. 22.In triangle ABC, angle A = 100° and angle B = 45°. What is angle C (in degrees)?
  23. 23.The two shorter sides of a right-angled triangle are 12 cm and 5 cm. How long is the longest side (in cm)?
  24. 24.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles (in degrees)?
  25. 25.In an isosceles triangle, the two equal angles are 26° each. What is the third angle (in degrees)?
  26. 26.In an isosceles triangle, the angle between the two equal sides is 108°. What is each of the other two angles (in degrees)?
  27. 27.The two interior opposite angles of a triangle are 46° and 54°. What is the exterior angle (in degrees)?
  28. 28.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles (in degrees)?
  29. 29.Can a triangle have sides of 9 cm, 6 cm and 9 cm? (a) No (b) Yes
  30. 30.In triangle ABC, angle A = 27° and angle B = 57°. What is angle C (in degrees)?
  31. 31.Can a triangle have sides of 10 cm, 8 cm and 14 cm? (a) No (b) Yes
  32. 32.Can a triangle have sides of 8 cm, 6 cm and 8 cm? (a) Yes (b) No
  33. 33.In triangle ABC, angle A = 35° and angle B = 25°. What is angle C (in degrees)?
  34. 34.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)?
  35. 35.The longest side of a right-angled triangle is 5 cm and one of the other sides is 3 cm. How long is the third side (in cm)?
  36. 36.In an isosceles triangle, the angle between the two equal sides is 114°. What is each of the other two angles (in degrees)?
  37. 37.In triangle ABC, angle A = 81° and angle B = 23°. What is angle C (in degrees)?
  38. 38.The longest side of a right-angled triangle is 30 cm and one of the other sides is 18 cm. How long is the third side (in cm)?
  39. 39.In triangle ABC, angle A = 56° and angle B = 92°. What is angle C (in degrees)?
  40. 40.In triangle ABC, angle A = 53° and angle B = 81°. What is angle C (in degrees)?

Answer key

  1. 17
  2. 54
  3. 74
  4. 80
  5. 72
  6. 104
  7. 36
  8. 32
  9. 13
  10. Yes
  11. No
  12. No
  13. 76
  14. 17
  15. 15
  16. 10
  17. 76
  18. 103
  19. 48
  20. 48
  21. 103
  22. 35
  23. 13
  24. 40
  25. 128
  26. 36
  27. 100
  28. 70
  29. Yes
  30. 96
  31. Yes
  32. Yes
  33. 120
  34. 3
  35. 4
  36. 33
  37. 76
  38. 24
  39. 32
  40. 46

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