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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 992 · 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 triangle ABC, angle A = 81° and angle B = 57°. What is angle C (in degrees)?
  2. 2.In a right-angled triangle, one of the other two angles is 16°. What is the third angle (in degrees)?
  3. 3.In an isosceles triangle, the two equal angles are 36° each. What is the third angle (in degrees)?
  4. 4.In triangle ABC, angle A = 91° and angle B = 24°. What is angle C (in degrees)?
  5. 5.Can a triangle have sides of 15 cm, 11 cm and 4 cm? (a) No (b) Yes
  6. 6.In triangle ABC, angle A = 82° and angle B = 23°. What is angle C (in degrees)?
  7. 7.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)?
  8. 8.In an isosceles triangle, the angle between the two equal sides is 48°. What is each of the other two angles (in degrees)?
  9. 9.Can a triangle have sides of 3 cm, 10 cm and 14 cm? (a) Yes (b) No
  10. 10.An exterior angle of a triangle is 76°. One of its two interior opposite angles is 23°. What is the other one (in degrees)?
  11. 11.The longest side of a right-angled triangle is 13 cm and one of the other sides is 12 cm. How long is the third side (in cm)?
  12. 12.In an isosceles triangle, the two equal angles are 65° each. What is the third angle (in degrees)?
  13. 13.Can a triangle have sides of 6 cm, 6 cm and 12 cm? (a) Yes (b) No
  14. 14.Can a triangle have sides of 2 cm, 6 cm and 5 cm? (a) Yes (b) No
  15. 15.The two interior opposite angles of a triangle are 40° and 75°. What is the exterior angle (in degrees)?
  16. 16.In a right-angled triangle, one of the other two angles is 25°. What is the third angle (in degrees)?
  17. 17.Can a triangle have sides of 7 cm, 2 cm and 5 cm? (a) No (b) Yes
  18. 18.An exterior angle of a triangle is 95°. One of its two interior opposite angles is 57°. What is the other one (in degrees)?
  19. 19.Can a triangle have sides of 16 cm, 8 cm and 8 cm? (a) Yes (b) No
  20. 20.The two shorter sides of a right-angled triangle are 12 cm and 9 cm. How long is the longest side (in cm)?
  21. 21.The two interior opposite angles of a triangle are 43° and 30°. What is the exterior angle (in degrees)?
  22. 22.The angles of a triangle are in the ratio 2 : 3 : 5. What is the smallest angle (in degrees)?
  23. 23.In an isosceles triangle, the two equal angles are 58° each. What is the third angle (in degrees)?
  24. 24.The longest side of a right-angled triangle is 30 cm and one of the other sides is 24 cm. How long is the third side (in cm)?
  25. 25.In a right-angled triangle, one of the other two angles is 10°. What is the third angle (in degrees)?
  26. 26.Can a triangle have sides of 7 cm, 18 cm and 7 cm? (a) No (b) Yes
  27. 27.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)?
  28. 28.The two shorter sides of a right-angled triangle are 24 cm and 7 cm. How long is the longest side (in cm)?
  29. 29.In an isosceles triangle, the angle between the two equal sides is 74°. What is each of the other two angles (in degrees)?
  30. 30.An exterior angle of a triangle is 132°. One of its two interior opposite angles is 78°. What is the other one (in degrees)?
  31. 31.In a right-angled triangle, one of the other two angles is 80°. What is the third angle (in degrees)?
  32. 32.The two shorter sides of a right-angled triangle are 15 cm and 20 cm. How long is the longest side (in cm)?
  33. 33.The two interior opposite angles of a triangle are 65° and 74°. What is the exterior angle (in degrees)?
  34. 34.The two interior opposite angles of a triangle are 65° and 77°. What is the exterior angle (in degrees)?
  35. 35.The two shorter sides of a right-angled triangle are 8 cm and 15 cm. How long is the longest side (in cm)?
  36. 36.In a right-angled triangle, one of the other two angles is 77°. What is the third angle (in degrees)?
  37. 37.The longest side of a right-angled triangle is 15 cm and one of the other sides is 12 cm. How long is the third side (in cm)?
  38. 38.In an isosceles triangle, the two equal angles are 56° each. What is the third angle (in degrees)?
  39. 39.An exterior angle of a triangle is 64°. One of its two interior opposite angles is 34°. What is the other one (in degrees)?
  40. 40.In triangle ABC, angle A = 90° and angle B = 28°. What is angle C (in degrees)?

Answer key

  1. 42
  2. 74
  3. 108
  4. 65
  5. No
  6. 75
  7. 4
  8. 66
  9. No
  10. 53
  11. 5
  12. 50
  13. No
  14. Yes
  15. 115
  16. 65
  17. No
  18. 38
  19. No
  20. 15
  21. 73
  22. 36
  23. 64
  24. 18
  25. 80
  26. No
  27. 8
  28. 25
  29. 53
  30. 54
  31. 10
  32. 25
  33. 139
  34. 142
  35. 17
  36. 13
  37. 9
  38. 68
  39. 30
  40. 62

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