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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 640 · 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.In an isosceles triangle, the angle between the two equal sides is 138°. What is each of the other two angles (in degrees)?
  2. 2.An exterior angle of a triangle is 59°. One of its two interior opposite angles is 33°. What is the other one (in degrees)?
  3. 3.Can a triangle have sides of 12 cm, 4 cm and 17 cm? (a) No (b) Yes
  4. 4.Can a triangle have sides of 5 cm, 8 cm and 12 cm? (a) No (b) Yes
  5. 5.Can a triangle have sides of 21 cm, 9 cm and 7 cm? (a) Yes (b) No
  6. 6.In an isosceles triangle, the angle between the two equal sides is 136°. What is each of the other two angles (in degrees)?
  7. 7.The two shorter sides of a right-angled triangle are 7 cm and 24 cm. How long is the longest side (in cm)?
  8. 8.Can a triangle have sides of 6 cm, 14 cm and 8 cm? (a) Yes (b) No
  9. 9.The angles of a triangle are in the ratio 5 : 6 : 7. What is the smallest angle (in degrees)?
  10. 10.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles (in degrees)?
  11. 11.In triangle ABC, angle A = 61° and angle B = 41°. What is angle C (in degrees)?
  12. 12.In triangle ABC, angle A = 27° and angle B = 83°. What is angle C (in degrees)?
  13. 13.Can a triangle have sides of 17 cm, 6 cm and 11 cm? (a) No (b) Yes
  14. 14.In a right-angled triangle, one of the other two angles is 13°. What is the third angle (in degrees)?
  15. 15.In triangle ABC, angle A = 66° and angle B = 79°. What is angle C (in degrees)?
  16. 16.In an isosceles triangle, the two equal angles are 20° each. What is the third angle (in degrees)?
  17. 17.In triangle ABC, angle A = 43° and angle B = 51°. What is angle C (in degrees)?
  18. 18.Can a triangle have sides of 11 cm, 10 cm and 21 cm? (a) No (b) Yes
  19. 19.An exterior angle of a triangle is 70°. One of its two interior opposite angles is 44°. What is the other one (in degrees)?
  20. 20.In triangle ABC, angle A = 35° and angle B = 88°. What is angle C (in degrees)?
  21. 21.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)?
  22. 22.In an isosceles triangle, the angle between the two equal sides is 152°. What is each of the other two angles (in degrees)?
  23. 23.Can a triangle have sides of 5 cm, 9 cm and 9 cm? (a) Yes (b) No
  24. 24.An exterior angle of a triangle is 88°. One of its two interior opposite angles is 36°. What is the other one (in degrees)?
  25. 25.An exterior angle of a triangle is 56°. One of its two interior opposite angles is 31°. What is the other one (in degrees)?
  26. 26.An exterior angle of a triangle is 115°. One of its two interior opposite angles is 42°. What is the other one (in degrees)?
  27. 27.Can a triangle have sides of 21 cm, 12 cm and 4 cm? (a) No (b) Yes
  28. 28.In an isosceles triangle, the angle between the two equal sides is 44°. What is each of the other two angles (in degrees)?
  29. 29.In an isosceles triangle, the two equal angles are 80° each. What is the third angle (in degrees)?
  30. 30.Can a triangle have sides of 10 cm, 12 cm and 15 cm? (a) No (b) Yes
  31. 31.An exterior angle of a triangle is 64°. One of its two interior opposite angles is 21°. What is the other one (in degrees)?
  32. 32.The angles of a triangle are in the ratio 5 : 6 : 7. What is the biggest angle (in degrees)?
  33. 33.The angles of a triangle are in the ratio 1 : 2 : 3. What is the smallest angle (in degrees)?
  34. 34.In a right-angled triangle, one of the other two angles is 73°. What is the third angle (in degrees)?
  35. 35.In an isosceles triangle, the angle between the two equal sides is 82°. What is each of the other two angles (in degrees)?
  36. 36.An exterior angle of a triangle is 108°. One of its two interior opposite angles is 71°. What is the other one (in degrees)?
  37. 37.The two shorter sides of a right-angled triangle are 8 cm and 15 cm. How long is the longest side (in cm)?
  38. 38.The longest side of a right-angled triangle is 39 cm and one of the other sides is 36 cm. How long is the third side (in cm)?
  39. 39.In triangle ABC, angle A = 43° and angle B = 59°. What is angle C (in degrees)?
  40. 40.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)?

Answer key

  1. 21
  2. 26
  3. No
  4. Yes
  5. No
  6. 22
  7. 25
  8. No
  9. 50
  10. 45
  11. 78
  12. 70
  13. No
  14. 77
  15. 35
  16. 140
  17. 86
  18. No
  19. 26
  20. 57
  21. 5
  22. 14
  23. Yes
  24. 52
  25. 25
  26. 73
  27. No
  28. 68
  29. 20
  30. Yes
  31. 43
  32. 70
  33. 30
  34. 17
  35. 49
  36. 37
  37. 17
  38. 15
  39. 78
  40. 24

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