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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 431 · 40 sums
TalentJR

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 angles of a triangle are in the ratio 3 : 4 : 5. What is the smallest angle (in degrees)?
  2. 2.In a right-angled triangle, one of the other two angles is 71°. What is the third angle (in degrees)?
  3. 3.In triangle ABC, angle A = 86° and angle B = 25°. What is angle C (in degrees)?
  4. 4.In triangle ABC, angle A = 87° and angle B = 32°. What is angle C (in degrees)?
  5. 5.In an isosceles triangle, the angle between the two equal sides is 98°. What is each of the other two angles (in degrees)?
  6. 6.In triangle ABC, angle A = 54° and angle B = 40°. What is angle C (in degrees)?
  7. 7.The two shorter sides of a right-angled triangle are 18 cm and 24 cm. How long is the longest side (in cm)?
  8. 8.In an isosceles triangle, the angle between the two equal sides is 86°. What is each of the other two angles (in degrees)?
  9. 9.An exterior angle of a triangle is 136°. One of its two interior opposite angles is 76°. What is the other one (in degrees)?
  10. 10.The two shorter sides of a right-angled triangle are 24 cm and 10 cm. How long is the longest side (in cm)?
  11. 11.In a right-angled triangle, one of the other two angles is 10°. What is the third angle (in degrees)?
  12. 12.In triangle ABC, angle A = 81° and angle B = 49°. What is angle C (in degrees)?
  13. 13.The angles of a triangle are in the ratio 1 : 2 : 3. What is the biggest angle (in degrees)?
  14. 14.The two interior opposite angles of a triangle are 53° and 52°. What is the exterior angle (in degrees)?
  15. 15.In an isosceles triangle, the two equal angles are 76° each. What is the third angle (in degrees)?
  16. 16.Can a triangle have sides of 13 cm, 10 cm and 8 cm? (a) No (b) Yes
  17. 17.In an isosceles triangle, the angle between the two equal sides is 24°. What is each of the other two angles (in degrees)?
  18. 18.In an isosceles triangle, the two equal angles are 61° each. What is the third angle (in degrees)?
  19. 19.The angles of a triangle are in the ratio 1 : 1 : 2. What is the smallest angle (in degrees)?
  20. 20.In an isosceles triangle, the angle between the two equal sides is 136°. What is each of the other two angles (in degrees)?
  21. 21.In triangle ABC, angle A = 40° and angle B = 112°. What is angle C (in degrees)?
  22. 22.In triangle ABC, angle A = 55° and angle B = 93°. What is angle C (in degrees)?
  23. 23.The longest side of a right-angled triangle is 13 cm and one of the other sides is 5 cm. How long is the third side (in cm)?
  24. 24.In an isosceles triangle, the two equal angles are 37° each. What is the third angle (in degrees)?
  25. 25.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles (in degrees)?
  26. 26.In a right-angled triangle, one of the other two angles is 18°. What is the third angle (in degrees)?
  27. 27.In triangle ABC, angle A = 100° and angle B = 20°. What is angle C (in degrees)?
  28. 28.Can a triangle have sides of 16 cm, 10 cm and 3 cm? (a) Yes (b) No
  29. 29.Can a triangle have sides of 10 cm, 13 cm and 7 cm? (a) No (b) Yes
  30. 30.The angles of a triangle are in the ratio 1 : 2 : 2. What is the smallest angle (in degrees)?
  31. 31.The two shorter sides of a right-angled triangle are 8 cm and 15 cm. How long is the longest side (in cm)?
  32. 32.The angles of a triangle are in the ratio 2 : 2 : 5. What is the biggest angle (in degrees)?
  33. 33.In triangle ABC, angle A = 23° and angle B = 66°. What is angle C (in degrees)?
  34. 34.In a right-angled triangle, one of the other two angles is 47°. What is the third angle (in degrees)?
  35. 35.An exterior angle of a triangle is 135°. One of its two interior opposite angles is 75°. What is the other one (in degrees)?
  36. 36.In a right-angled triangle, one of the other two angles is 73°. What is the third angle (in degrees)?
  37. 37.An exterior angle of a triangle is 84°. One of its two interior opposite angles is 32°. What is the other one (in degrees)?
  38. 38.The angles of a triangle are in the ratio 4 : 5 : 6. What is the biggest angle (in degrees)?
  39. 39.An exterior angle of a triangle is 46°. One of its two interior opposite angles is 21°. What is the other one (in degrees)?
  40. 40.An exterior angle of a triangle is 100°. One of its two interior opposite angles is 27°. What is the other one (in degrees)?

Answer key

  1. 45
  2. 19
  3. 69
  4. 61
  5. 41
  6. 86
  7. 30
  8. 47
  9. 60
  10. 26
  11. 80
  12. 50
  13. 90
  14. 105
  15. 28
  16. Yes
  17. 78
  18. 58
  19. 45
  20. 22
  21. 28
  22. 32
  23. 12
  24. 106
  25. 80
  26. 72
  27. 60
  28. No
  29. Yes
  30. 36
  31. 17
  32. 100
  33. 91
  34. 43
  35. 60
  36. 17
  37. 52
  38. 72
  39. 25
  40. 73

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