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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 784 · 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 8 cm. How long is the third side (in cm)?
  2. 2.The two shorter sides of a right-angled triangle are 12 cm and 9 cm. How long is the longest side (in cm)?
  3. 3.The longest side of a right-angled triangle is 25 cm and one of the other sides is 24 cm. How long is the third side (in cm)?
  4. 4.The angles of a triangle are in the ratio 1 : 2 : 2. What is the smallest angle (in degrees)?
  5. 5.In an isosceles triangle, the angle between the two equal sides is 64°. What is each of the other two angles (in degrees)?
  6. 6.In an isosceles triangle, the angle between the two equal sides is 104°. What is each of the other two angles (in degrees)?
  7. 7.The two interior opposite angles of a triangle are 28° and 35°. What is the exterior angle (in degrees)?
  8. 8.In a right-angled triangle, one of the other two angles is 26°. What is the third angle (in degrees)?
  9. 9.An exterior angle of a triangle is 73°. One of its two interior opposite angles is 26°. What is the other one (in degrees)?
  10. 10.In triangle ABC, angle A = 40° and angle B = 111°. What is angle C (in degrees)?
  11. 11.The angles of a triangle are in the ratio 2 : 3 : 4. What is the biggest angle (in degrees)?
  12. 12.In an isosceles triangle, the two equal angles are 60° each. What is the third angle (in degrees)?
  13. 13.The two shorter sides of a right-angled triangle are 15 cm and 36 cm. How long is the longest side (in cm)?
  14. 14.In an isosceles triangle, the two equal angles are 37° each. What is the third angle (in degrees)?
  15. 15.The angles of a triangle are in the ratio 1 : 2 : 6. What is the biggest angle (in degrees)?
  16. 16.Can a triangle have sides of 6 cm, 2 cm and 10 cm? (a) Yes (b) No
  17. 17.In an isosceles triangle, the two equal angles are 32° each. What is the third angle (in degrees)?
  18. 18.In an isosceles triangle, the two equal angles are 22° each. What is the third angle (in degrees)?
  19. 19.In a right-angled triangle, one of the other two angles is 24°. What is the third angle (in degrees)?
  20. 20.In triangle ABC, angle A = 31° and angle B = 76°. What is angle C (in degrees)?
  21. 21.The two interior opposite angles of a triangle are 73° and 57°. What is the exterior angle (in degrees)?
  22. 22.An exterior angle of a triangle is 130°. One of its two interior opposite angles is 75°. What is the other one (in degrees)?
  23. 23.Can a triangle have sides of 2 cm, 9 cm and 12 cm? (a) Yes (b) No
  24. 24.In triangle ABC, angle A = 44° and angle B = 97°. What is angle C (in degrees)?
  25. 25.In triangle ABC, angle A = 50° and angle B = 58°. What is angle C (in degrees)?
  26. 26.In a right-angled triangle, one of the other two angles is 36°. What is the third angle (in degrees)?
  27. 27.In an isosceles triangle, the two equal angles are 65° each. What is the third angle (in degrees)?
  28. 28.The two interior opposite angles of a triangle are 45° and 46°. What is the exterior angle (in degrees)?
  29. 29.Can a triangle have sides of 2 cm, 12 cm and 12 cm? (a) No (b) Yes
  30. 30.An exterior angle of a triangle is 110°. One of its two interior opposite angles is 40°. What is the other one (in degrees)?
  31. 31.In an isosceles triangle, the angle between the two equal sides is 138°. What is each of the other two angles (in degrees)?
  32. 32.In a right-angled triangle, one of the other two angles is 21°. What is the third angle (in degrees)?
  33. 33.In triangle ABC, angle A = 59° and angle B = 49°. What is angle C (in degrees)?
  34. 34.The angles of a triangle are in the ratio 2 : 7 : 9. What is the biggest angle (in degrees)?
  35. 35.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)?
  36. 36.In triangle ABC, angle A = 79° and angle B = 65°. What is angle C (in degrees)?
  37. 37.The two interior opposite angles of a triangle are 27° and 78°. What is the exterior angle (in degrees)?
  38. 38.In an isosceles triangle, the two equal angles are 39° each. What is the third angle (in degrees)?
  39. 39.Can a triangle have sides of 12 cm, 23 cm and 6 cm? (a) No (b) Yes
  40. 40.Can a triangle have sides of 11 cm, 6 cm and 17 cm? (a) Yes (b) No

Answer key

  1. 15
  2. 15
  3. 7
  4. 36
  5. 58
  6. 38
  7. 63
  8. 64
  9. 47
  10. 29
  11. 80
  12. 60
  13. 39
  14. 106
  15. 120
  16. No
  17. 116
  18. 136
  19. 66
  20. 73
  21. 130
  22. 55
  23. No
  24. 39
  25. 72
  26. 54
  27. 50
  28. 91
  29. Yes
  30. 70
  31. 21
  32. 69
  33. 72
  34. 90
  35. 8
  36. 36
  37. 105
  38. 102
  39. No
  40. No

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