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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 61 · 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 two shorter sides of a right-angled triangle are 4 cm and 3 cm. How long is the longest side (in cm)?
  2. 2.The angles of a triangle are in the ratio 1 : 1 : 2. What is the smallest angle (in degrees)?
  3. 3.In triangle ABC, angle A = 70° and angle B = 71°. What is angle C (in degrees)?
  4. 4.In an isosceles triangle, the angle between the two equal sides is 86°. What is each of the other two angles (in degrees)?
  5. 5.In an isosceles triangle, the angle between the two equal sides is 126°. What is each of the other two angles (in degrees)?
  6. 6.Can a triangle have sides of 17 cm, 8 cm and 7 cm? (a) No (b) Yes
  7. 7.In an isosceles triangle, the two equal angles are 83° each. What is the third angle (in degrees)?
  8. 8.In triangle ABC, angle A = 40° and angle B = 103°. What is angle C (in degrees)?
  9. 9.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles (in degrees)?
  10. 10.In a right-angled triangle, one of the other two angles is 15°. What is the third angle (in degrees)?
  11. 11.The two interior opposite angles of a triangle are 64° and 32°. What is the exterior angle (in degrees)?
  12. 12.An exterior angle of a triangle is 120°. One of its two interior opposite angles is 55°. What is the other one (in degrees)?
  13. 13.The angles of a triangle are in the ratio 2 : 7 : 9. What is the biggest angle (in degrees)?
  14. 14.In a right-angled triangle, one of the other two angles is 11°. What is the third angle (in degrees)?
  15. 15.Can a triangle have sides of 4 cm, 7 cm and 10 cm? (a) Yes (b) No
  16. 16.An exterior angle of a triangle is 69°. One of its two interior opposite angles is 44°. What is the other one (in degrees)?
  17. 17.An exterior angle of a triangle is 145°. One of its two interior opposite angles is 71°. What is the other one (in degrees)?
  18. 18.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles (in degrees)?
  19. 19.In a right-angled triangle, one of the other two angles is 28°. What is the third angle (in degrees)?
  20. 20.An exterior angle of a triangle is 97°. One of its two interior opposite angles is 59°. What is the other one (in degrees)?
  21. 21.An exterior angle of a triangle is 139°. One of its two interior opposite angles is 63°. What is the other one (in degrees)?
  22. 22.An exterior angle of a triangle is 95°. One of its two interior opposite angles is 23°. What is the other one (in degrees)?
  23. 23.Can a triangle have sides of 12 cm, 6 cm and 6 cm? (a) No (b) Yes
  24. 24.An exterior angle of a triangle is 84°. One of its two interior opposite angles is 21°. What is the other one (in degrees)?
  25. 25.Can a triangle have sides of 6 cm, 12 cm and 4 cm? (a) Yes (b) No
  26. 26.The angles of a triangle are in the ratio 5 : 6 : 7. What is the biggest angle (in degrees)?
  27. 27.Can a triangle have sides of 5 cm, 4 cm and 2 cm? (a) No (b) Yes
  28. 28.In an isosceles triangle, the two equal angles are 39° each. What is the third angle (in degrees)?
  29. 29.The angles of a triangle are in the ratio 1 : 4 : 5. What is the smallest angle (in degrees)?
  30. 30.An exterior angle of a triangle is 126°. One of its two interior opposite angles is 66°. What is the other one (in degrees)?
  31. 31.In a right-angled triangle, one of the other two angles is 57°. What is the third angle (in degrees)?
  32. 32.Can a triangle have sides of 23 cm, 11 cm and 8 cm? (a) Yes (b) No
  33. 33.The two shorter sides of a right-angled triangle are 15 cm and 8 cm. How long is the longest side (in cm)?
  34. 34.The two shorter sides of a right-angled triangle are 6 cm and 8 cm. How long is the longest side (in cm)?
  35. 35.The two interior opposite angles of a triangle are 80° and 34°. What is the exterior angle (in degrees)?
  36. 36.In a right-angled triangle, one of the other two angles is 45°. What is the third angle (in degrees)?
  37. 37.The two shorter sides of a right-angled triangle are 7 cm and 24 cm. How long is the longest side (in cm)?
  38. 38.An exterior angle of a triangle is 92°. One of its two interior opposite angles is 71°. What is the other one (in degrees)?
  39. 39.In triangle ABC, angle A = 69° and angle B = 87°. What is angle C (in degrees)?
  40. 40.The angles of a triangle are in the ratio 1 : 3 : 5. What is the smallest angle (in degrees)?

Answer key

  1. 5
  2. 45
  3. 39
  4. 47
  5. 27
  6. No
  7. 14
  8. 37
  9. 55
  10. 75
  11. 96
  12. 65
  13. 90
  14. 79
  15. Yes
  16. 25
  17. 74
  18. 25
  19. 62
  20. 38
  21. 76
  22. 72
  23. No
  24. 63
  25. No
  26. 70
  27. Yes
  28. 102
  29. 18
  30. 60
  31. 33
  32. No
  33. 17
  34. 10
  35. 114
  36. 45
  37. 25
  38. 21
  39. 24
  40. 20

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