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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 684 · 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 24 cm and 18 cm. How long is the longest side (in cm)?
  2. 2.An exterior angle of a triangle is 69°. One of its two interior opposite angles is 46°. What is the other one (in degrees)?
  3. 3.In an isosceles triangle, the angle between the two equal sides is 28°. What is each of the other two angles (in degrees)?
  4. 4.The angles of a triangle are in the ratio 3 : 4 : 5. What is the smallest angle (in degrees)?
  5. 5.Can a triangle have sides of 10 cm, 9 cm and 18 cm? (a) Yes (b) No
  6. 6.The two interior opposite angles of a triangle are 55° and 43°. What is the exterior angle (in degrees)?
  7. 7.Can a triangle have sides of 7 cm, 7 cm and 6 cm? (a) Yes (b) No
  8. 8.The angles of a triangle are in the ratio 2 : 3 : 4. What is the smallest angle (in degrees)?
  9. 9.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)?
  10. 10.An exterior angle of a triangle is 83°. One of its two interior opposite angles is 58°. What is the other one (in degrees)?
  11. 11.The two shorter sides of a right-angled triangle are 6 cm and 8 cm. How long is the longest side (in cm)?
  12. 12.In an isosceles triangle, the two equal angles are 75° each. What is the third angle (in degrees)?
  13. 13.In an isosceles triangle, the two equal angles are 54° each. What is the third angle (in degrees)?
  14. 14.The angles of a triangle are in the ratio 1 : 2 : 3. What is the smallest angle (in degrees)?
  15. 15.The two shorter sides of a right-angled triangle are 15 cm and 8 cm. How long is the longest side (in cm)?
  16. 16.Can a triangle have sides of 10 cm, 23 cm and 12 cm? (a) Yes (b) No
  17. 17.The angles of a triangle are in the ratio 2 : 3 : 5. What is the biggest angle (in degrees)?
  18. 18.In triangle ABC, angle A = 59° and angle B = 60°. What is angle C (in degrees)?
  19. 19.In an isosceles triangle, the angle between the two equal sides is 124°. What is each of the other two angles (in degrees)?
  20. 20.The longest side of a right-angled triangle is 20 cm and one of the other sides is 12 cm. How long is the third side (in cm)?
  21. 21.The angles of a triangle are in the ratio 2 : 3 : 5. What is the smallest angle (in degrees)?
  22. 22.The two shorter sides of a right-angled triangle are 8 cm and 15 cm. How long is the longest side (in cm)?
  23. 23.In a right-angled triangle, one of the other two angles is 37°. What is the third angle (in degrees)?
  24. 24.An exterior angle of a triangle is 112°. One of its two interior opposite angles is 43°. What is the other one (in degrees)?
  25. 25.In triangle ABC, angle A = 80° and angle B = 31°. What is angle C (in degrees)?
  26. 26.In triangle ABC, angle A = 94° and angle B = 36°. What is angle C (in degrees)?
  27. 27.The two interior opposite angles of a triangle are 22° and 51°. What is the exterior angle (in degrees)?
  28. 28.Can a triangle have sides of 9 cm, 12 cm and 25 cm? (a) No (b) Yes
  29. 29.An exterior angle of a triangle is 114°. One of its two interior opposite angles is 61°. What is the other one (in degrees)?
  30. 30.Can a triangle have sides of 5 cm, 14 cm and 9 cm? (a) No (b) Yes
  31. 31.An exterior angle of a triangle is 99°. One of its two interior opposite angles is 48°. What is the other one (in degrees)?
  32. 32.In a right-angled triangle, one of the other two angles is 54°. What is the third angle (in degrees)?
  33. 33.The angles of a triangle are in the ratio 1 : 1 : 2. What is the biggest angle (in degrees)?
  34. 34.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles (in degrees)?
  35. 35.In an isosceles triangle, the two equal angles are 60° each. What is the third angle (in degrees)?
  36. 36.The longest side of a right-angled triangle is 26 cm and one of the other sides is 10 cm. How long is the third side (in cm)?
  37. 37.The angles of a triangle are in the ratio 3 : 5 : 7. What is the biggest angle (in degrees)?
  38. 38.In triangle ABC, angle A = 38° and angle B = 35°. What is angle C (in degrees)?
  39. 39.In a right-angled triangle, one of the other two angles is 26°. What is the third angle (in degrees)?
  40. 40.In a right-angled triangle, one of the other two angles is 28°. What is the third angle (in degrees)?

Answer key

  1. 30
  2. 23
  3. 76
  4. 45
  5. Yes
  6. 98
  7. Yes
  8. 40
  9. 24
  10. 25
  11. 10
  12. 30
  13. 72
  14. 30
  15. 17
  16. No
  17. 90
  18. 61
  19. 28
  20. 16
  21. 36
  22. 17
  23. 53
  24. 69
  25. 69
  26. 50
  27. 73
  28. No
  29. 53
  30. No
  31. 51
  32. 36
  33. 90
  34. 50
  35. 60
  36. 24
  37. 84
  38. 107
  39. 64
  40. 62

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