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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 761 · 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 longest side of a right-angled triangle is 25 cm and one of the other sides is 15 cm. How long is the third side (in cm)?
  2. 2.The two interior opposite angles of a triangle are 59° and 32°. What is the exterior angle (in degrees)?
  3. 3.In a right-angled triangle, one of the other two angles is 53°. What is the third angle (in degrees)?
  4. 4.In a right-angled triangle, one of the other two angles is 50°. What is the third angle (in degrees)?
  5. 5.An exterior angle of a triangle is 56°. One of its two interior opposite angles is 33°. What is the other one (in degrees)?
  6. 6.In triangle ABC, angle A = 87° and angle B = 70°. 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 146°. What is each of the other two angles (in degrees)?
  9. 9.In a right-angled triangle, one of the other two angles is 20°. What is the third angle (in degrees)?
  10. 10.In a right-angled triangle, one of the other two angles is 19°. What is the third angle (in degrees)?
  11. 11.In a right-angled triangle, one of the other two angles is 24°. What is the third angle (in degrees)?
  12. 12.In triangle ABC, angle A = 37° and angle B = 53°. What is angle C (in degrees)?
  13. 13.In a right-angled triangle, one of the other two angles is 32°. What is the third angle (in degrees)?
  14. 14.In a right-angled triangle, one of the other two angles is 18°. What is the third angle (in degrees)?
  15. 15.In triangle ABC, angle A = 96° and angle B = 42°. What is angle C (in degrees)?
  16. 16.In an isosceles triangle, the angle between the two equal sides is 156°. What is each of the other two angles (in degrees)?
  17. 17.In triangle ABC, angle A = 28° and angle B = 65°. What is angle C (in degrees)?
  18. 18.In triangle ABC, angle A = 42° and angle B = 75°. What is angle C (in degrees)?
  19. 19.The two interior opposite angles of a triangle are 32° and 68°. What is the exterior angle (in degrees)?
  20. 20.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)?
  21. 21.The angles of a triangle are in the ratio 2 : 7 : 9. What is the smallest angle (in degrees)?
  22. 22.The two interior opposite angles of a triangle are 67° and 42°. What is the exterior angle (in degrees)?
  23. 23.Can a triangle have sides of 8 cm, 12 cm and 10 cm? (a) Yes (b) No
  24. 24.In triangle ABC, angle A = 70° and angle B = 21°. What is angle C (in degrees)?
  25. 25.Can a triangle have sides of 10 cm, 4 cm and 10 cm? (a) Yes (b) No
  26. 26.An exterior angle of a triangle is 82°. One of its two interior opposite angles is 37°. What is the other one (in degrees)?
  27. 27.In triangle ABC, angle A = 35° and angle B = 78°. What is angle C (in degrees)?
  28. 28.In a right-angled triangle, one of the other two angles is 37°. 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.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)?
  31. 31.In triangle ABC, angle A = 41° and angle B = 70°. What is angle C (in degrees)?
  32. 32.The two shorter sides of a right-angled triangle are 7 cm and 24 cm. How long is the longest side (in cm)?
  33. 33.In a right-angled triangle, one of the other two angles is 66°. What is the third angle (in degrees)?
  34. 34.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)?
  35. 35.In a right-angled triangle, one of the other two angles is 57°. What is the third angle (in degrees)?
  36. 36.An exterior angle of a triangle is 104°. One of its two interior opposite angles is 24°. What is the other one (in degrees)?
  37. 37.In a right-angled triangle, one of the other two angles is 43°. What is the third angle (in degrees)?
  38. 38.In triangle ABC, angle A = 78° and angle B = 70°. What is angle C (in degrees)?
  39. 39.In a right-angled triangle, one of the other two angles is 68°. What is the third angle (in degrees)?
  40. 40.Can a triangle have sides of 7 cm, 17 cm and 9 cm? (a) No (b) Yes

Answer key

  1. 20
  2. 91
  3. 37
  4. 40
  5. 23
  6. 23
  7. 4
  8. 17
  9. 70
  10. 71
  11. 66
  12. 90
  13. 58
  14. 72
  15. 42
  16. 12
  17. 87
  18. 63
  19. 100
  20. 3
  21. 20
  22. 109
  23. Yes
  24. 89
  25. Yes
  26. 45
  27. 67
  28. 53
  29. 17
  30. 12
  31. 69
  32. 25
  33. 24
  34. 24
  35. 33
  36. 80
  37. 47
  38. 32
  39. 22
  40. No

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