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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 755 · 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 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)?
  2. 2.An exterior angle of a triangle is 134°. One of its two interior opposite angles is 66°. What is the other one (in degrees)?
  3. 3.In an isosceles triangle, the angle between the two equal sides is 158°. What is each of the other two angles (in degrees)?
  4. 4.In triangle ABC, angle A = 94° and angle B = 58°. What is angle C (in degrees)?
  5. 5.The two shorter sides of a right-angled triangle are 12 cm and 16 cm. How long is the longest side (in cm)?
  6. 6.An exterior angle of a triangle is 64°. One of its two interior opposite angles is 42°. What is the other one (in degrees)?
  7. 7.In triangle ABC, angle A = 41° and angle B = 21°. What is angle C (in degrees)?
  8. 8.The angles of a triangle are in the ratio 2 : 3 : 5. What is the biggest angle (in degrees)?
  9. 9.In a right-angled triangle, one of the other two angles is 67°. What is the third angle (in degrees)?
  10. 10.In triangle ABC, angle A = 20° and angle B = 20°. What is angle C (in degrees)?
  11. 11.An exterior angle of a triangle is 104°. One of its two interior opposite angles is 68°. What is the other one (in degrees)?
  12. 12.The longest side of a right-angled triangle is 5 cm and one of the other sides is 4 cm. How long is the third side (in cm)?
  13. 13.The angles of a triangle are in the ratio 5 : 6 : 7. What is the biggest angle (in degrees)?
  14. 14.In an isosceles triangle, the two equal angles are 74° each. What is the third angle (in degrees)?
  15. 15.An exterior angle of a triangle is 107°. One of its two interior opposite angles is 50°. What is the other one (in degrees)?
  16. 16.In a right-angled triangle, one of the other two angles is 78°. What is the third angle (in degrees)?
  17. 17.In triangle ABC, angle A = 36° and angle B = 39°. What is angle C (in degrees)?
  18. 18.In a right-angled triangle, one of the other two angles is 73°. What is the third angle (in degrees)?
  19. 19.The two shorter sides of a right-angled triangle are 15 cm and 8 cm. How long is the longest side (in cm)?
  20. 20.In triangle ABC, angle A = 46° and angle B = 31°. What is angle C (in degrees)?
  21. 21.The angles of a triangle are in the ratio 2 : 2 : 5. What is the biggest angle (in degrees)?
  22. 22.The two interior opposite angles of a triangle are 55° and 62°. What is the exterior angle (in degrees)?
  23. 23.Can a triangle have sides of 11 cm, 12 cm and 7 cm? (a) No (b) Yes
  24. 24.Can a triangle have sides of 21 cm, 11 cm and 10 cm? (a) Yes (b) No
  25. 25.In an isosceles triangle, the two equal angles are 59° each. What is the third angle (in degrees)?
  26. 26.Can a triangle have sides of 11 cm, 25 cm and 10 cm? (a) No (b) Yes
  27. 27.Can a triangle have sides of 4 cm, 12 cm and 3 cm? (a) No (b) Yes
  28. 28.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles (in degrees)?
  29. 29.An exterior angle of a triangle is 116°. One of its two interior opposite angles is 68°. What is the other one (in degrees)?
  30. 30.Can a triangle have sides of 4 cm, 4 cm and 4 cm? (a) Yes (b) No
  31. 31.Can a triangle have sides of 12 cm, 15 cm and 10 cm? (a) No (b) Yes
  32. 32.In a right-angled triangle, one of the other two angles is 55°. What is the third angle (in degrees)?
  33. 33.In a right-angled triangle, one of the other two angles is 20°. What is the third angle (in degrees)?
  34. 34.In triangle ABC, angle A = 66° and angle B = 85°. What is angle C (in degrees)?
  35. 35.An exterior angle of a triangle is 101°. One of its two interior opposite angles is 70°. What is the other one (in degrees)?
  36. 36.In a right-angled triangle, one of the other two angles is 76°. What is the third angle (in degrees)?
  37. 37.The angles of a triangle are in the ratio 3 : 5 : 7. What is the smallest angle (in degrees)?
  38. 38.In a right-angled triangle, one of the other two angles is 41°. What is the third angle (in degrees)?
  39. 39.The two shorter sides of a right-angled triangle are 24 cm and 7 cm. How long is the longest side (in cm)?
  40. 40.An exterior angle of a triangle is 75°. One of its two interior opposite angles is 47°. What is the other one (in degrees)?

Answer key

  1. 8
  2. 68
  3. 11
  4. 28
  5. 20
  6. 22
  7. 118
  8. 90
  9. 23
  10. 140
  11. 36
  12. 3
  13. 70
  14. 32
  15. 57
  16. 12
  17. 105
  18. 17
  19. 17
  20. 103
  21. 100
  22. 117
  23. Yes
  24. No
  25. 62
  26. No
  27. No
  28. 45
  29. 48
  30. Yes
  31. Yes
  32. 35
  33. 70
  34. 29
  35. 31
  36. 14
  37. 36
  38. 49
  39. 25
  40. 28

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