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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 552 · 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 2 : 7 : 9. What is the smallest angle (in degrees)?
  2. 2.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)?
  3. 3.In an isosceles triangle, the angle between the two equal sides is 76°. What is each of the other two angles (in degrees)?
  4. 4.The angles of a triangle are in the ratio 1 : 2 : 2. What is the smallest angle (in degrees)?
  5. 5.The angles of a triangle are in the ratio 2 : 7 : 9. What is the biggest angle (in degrees)?
  6. 6.The two shorter sides of a right-angled triangle are 15 cm and 20 cm. How long is the longest side (in cm)?
  7. 7.The angles of a triangle are in the ratio 1 : 1 : 2. What is the biggest angle (in degrees)?
  8. 8.The two shorter sides of a right-angled triangle are 24 cm and 7 cm. How long is the longest side (in cm)?
  9. 9.The angles of a triangle are in the ratio 2 : 2 : 5. What is the biggest angle (in degrees)?
  10. 10.The two interior opposite angles of a triangle are 34° and 30°. What is the exterior angle (in degrees)?
  11. 11.In a right-angled triangle, one of the other two angles is 31°. What is the third angle (in degrees)?
  12. 12.Can a triangle have sides of 23 cm, 12 cm and 9 cm? (a) No (b) Yes
  13. 13.In triangle ABC, angle A = 81° and angle B = 49°. What is angle C (in degrees)?
  14. 14.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles (in degrees)?
  15. 15.The angles of a triangle are in the ratio 1 : 4 : 5. What is the biggest angle (in degrees)?
  16. 16.In a right-angled triangle, one of the other two angles is 66°. What is the third angle (in degrees)?
  17. 17.In triangle ABC, angle A = 94° and angle B = 27°. What is angle C (in degrees)?
  18. 18.An exterior angle of a triangle is 93°. One of its two interior opposite angles is 68°. What is the other one (in degrees)?
  19. 19.An exterior angle of a triangle is 104°. One of its two interior opposite angles is 35°. What is the other one (in degrees)?
  20. 20.Can a triangle have sides of 10 cm, 7 cm and 9 cm? (a) No (b) Yes
  21. 21.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)?
  22. 22.In a right-angled triangle, one of the other two angles is 45°. What is the third angle (in degrees)?
  23. 23.Can a triangle have sides of 6 cm, 10 cm and 18 cm? (a) Yes (b) No
  24. 24.Can a triangle have sides of 2 cm, 4 cm and 4 cm? (a) Yes (b) No
  25. 25.In an isosceles triangle, the two equal angles are 54° each. What is the third angle (in degrees)?
  26. 26.Can a triangle have sides of 13 cm, 3 cm and 7 cm? (a) No (b) Yes
  27. 27.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)?
  28. 28.An exterior angle of a triangle is 66°. One of its two interior opposite angles is 28°. What is the other one (in degrees)?
  29. 29.The two shorter sides of a right-angled triangle are 24 cm and 10 cm. How long is the longest side (in cm)?
  30. 30.An exterior angle of a triangle is 104°. One of its two interior opposite angles is 49°. What is the other one (in degrees)?
  31. 31.In a right-angled triangle, one of the other two angles is 24°. What is the third angle (in degrees)?
  32. 32.Can a triangle have sides of 10 cm, 6 cm and 8 cm? (a) No (b) Yes
  33. 33.In triangle ABC, angle A = 27° and angle B = 98°. What is angle C (in degrees)?
  34. 34.An exterior angle of a triangle is 100°. One of its two interior opposite angles is 57°. What is the other one (in degrees)?
  35. 35.In triangle ABC, angle A = 77° and angle B = 49°. What is angle C (in degrees)?
  36. 36.In an isosceles triangle, the two equal angles are 77° each. What is the third angle (in degrees)?
  37. 37.In triangle ABC, angle A = 40° and angle B = 40°. What is angle C (in degrees)?
  38. 38.In an isosceles triangle, the two equal angles are 43° each. What is the third angle (in degrees)?
  39. 39.In a right-angled triangle, one of the other two angles is 57°. What is the third angle (in degrees)?
  40. 40.The longest side of a right-angled triangle is 25 cm and one of the other sides is 20 cm. How long is the third side (in cm)?

Answer key

  1. 20
  2. 5
  3. 52
  4. 36
  5. 90
  6. 25
  7. 90
  8. 25
  9. 100
  10. 64
  11. 59
  12. No
  13. 50
  14. 20
  15. 90
  16. 24
  17. 59
  18. 25
  19. 69
  20. Yes
  21. 12
  22. 45
  23. No
  24. Yes
  25. 72
  26. No
  27. 18
  28. 38
  29. 26
  30. 55
  31. 66
  32. Yes
  33. 55
  34. 43
  35. 54
  36. 26
  37. 100
  38. 94
  39. 33
  40. 15

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