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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 840 · 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 angles of a triangle are in the ratio 2 : 3 : 4. What is the biggest angle (in degrees)?
  2. 2.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)?
  3. 3.The two shorter sides of a right-angled triangle are 15 cm and 8 cm. How long is the longest side (in cm)?
  4. 4.Can a triangle have sides of 9 cm, 9 cm and 21 cm? (a) Yes (b) No
  5. 5.In a right-angled triangle, one of the other two angles is 41°. What is the third angle (in degrees)?
  6. 6.In triangle ABC, angle A = 89° and angle B = 32°. What is angle C (in degrees)?
  7. 7.The longest side of a right-angled triangle is 25 cm and one of the other sides is 7 cm. How long is the third side (in cm)?
  8. 8.Can a triangle have sides of 17 cm, 8 cm and 11 cm? (a) No (b) Yes
  9. 9.In an isosceles triangle, the two equal angles are 46° each. What is the third angle (in degrees)?
  10. 10.In triangle ABC, angle A = 44° and angle B = 93°. What is angle C (in degrees)?
  11. 11.In a right-angled triangle, one of the other two angles is 25°. What is the third angle (in degrees)?
  12. 12.An exterior angle of a triangle is 109°. One of its two interior opposite angles is 47°. What is the other one (in degrees)?
  13. 13.An exterior angle of a triangle is 89°. One of its two interior opposite angles is 48°. What is the other one (in degrees)?
  14. 14.The angles of a triangle are in the ratio 1 : 2 : 3. What is the biggest angle (in degrees)?
  15. 15.The two interior opposite angles of a triangle are 65° and 62°. What is the exterior angle (in degrees)?
  16. 16.In triangle ABC, angle A = 76° and angle B = 23°. What is angle C (in degrees)?
  17. 17.In triangle ABC, angle A = 58° and angle B = 94°. What is angle C (in degrees)?
  18. 18.The angles of a triangle are in the ratio 2 : 7 : 9. What is the biggest angle (in degrees)?
  19. 19.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)?
  20. 20.Can a triangle have sides of 2 cm, 3 cm and 4 cm? (a) Yes (b) No
  21. 21.Can a triangle have sides of 9 cm, 6 cm and 4 cm? (a) No (b) Yes
  22. 22.An exterior angle of a triangle is 78°. One of its two interior opposite angles is 28°. What is the other one (in degrees)?
  23. 23.The longest side of a right-angled triangle is 17 cm and one of the other sides is 8 cm. How long is the third side (in cm)?
  24. 24.An exterior angle of a triangle is 78°. One of its two interior opposite angles is 56°. What is the other one (in degrees)?
  25. 25.In a right-angled triangle, one of the other two angles is 13°. What is the third angle (in degrees)?
  26. 26.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)?
  27. 27.Can a triangle have sides of 7 cm, 6 cm and 16 cm? (a) No (b) Yes
  28. 28.In triangle ABC, angle A = 31° and angle B = 83°. What is angle C (in degrees)?
  29. 29.Can a triangle have sides of 8 cm, 8 cm and 4 cm? (a) No (b) Yes
  30. 30.An exterior angle of a triangle is 69°. One of its two interior opposite angles is 38°. What is the other one (in degrees)?
  31. 31.The angles of a triangle are in the ratio 1 : 2 : 2. What is the biggest angle (in degrees)?
  32. 32.In a right-angled triangle, one of the other two angles is 79°. What is the third angle (in degrees)?
  33. 33.In triangle ABC, angle A = 20° and angle B = 79°. What is angle C (in degrees)?
  34. 34.In an isosceles triangle, the angle between the two equal sides is 72°. What is each of the other two angles (in degrees)?
  35. 35.In a right-angled triangle, one of the other two angles is 14°. What is the third angle (in degrees)?
  36. 36.In a right-angled triangle, one of the other two angles is 65°. What is the third angle (in degrees)?
  37. 37.Can a triangle have sides of 20 cm, 9 cm and 9 cm? (a) No (b) Yes
  38. 38.The angles of a triangle are in the ratio 3 : 4 : 5. What is the smallest angle (in degrees)?
  39. 39.In a right-angled triangle, one of the other two angles is 21°. What is the third angle (in degrees)?
  40. 40.In an isosceles triangle, the angle between the two equal sides is 24°. What is each of the other two angles (in degrees)?

Answer key

  1. 80
  2. 8
  3. 17
  4. No
  5. 49
  6. 59
  7. 24
  8. Yes
  9. 88
  10. 43
  11. 65
  12. 62
  13. 41
  14. 90
  15. 127
  16. 81
  17. 28
  18. 90
  19. 18
  20. Yes
  21. Yes
  22. 50
  23. 15
  24. 22
  25. 77
  26. 12
  27. No
  28. 66
  29. Yes
  30. 31
  31. 72
  32. 11
  33. 81
  34. 54
  35. 76
  36. 25
  37. No
  38. 45
  39. 69
  40. 78

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