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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 609 · 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 39 cm and one of the other sides is 15 cm. How long is the third side (in cm)?
  2. 2.In a right-angled triangle, one of the other two angles is 52°. What is the third angle (in degrees)?
  3. 3.In triangle ABC, angle A = 77° and angle B = 73°. What is angle C (in degrees)?
  4. 4.In a right-angled triangle, one of the other two angles is 73°. What is the third angle (in degrees)?
  5. 5.The angles of a triangle are in the ratio 2 : 2 : 5. What is the smallest angle (in degrees)?
  6. 6.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)?
  7. 7.In a right-angled triangle, one of the other two angles is 44°. What is the third angle (in degrees)?
  8. 8.The angles of a triangle are in the ratio 5 : 6 : 7. What is the biggest angle (in degrees)?
  9. 9.In an isosceles triangle, the angle between the two equal sides is 38°. What is each of the other two angles (in degrees)?
  10. 10.In triangle ABC, angle A = 37° and angle B = 111°. What is angle C (in degrees)?
  11. 11.The two interior opposite angles of a triangle are 54° and 36°. What is the exterior angle (in degrees)?
  12. 12.An exterior angle of a triangle is 90°. One of its two interior opposite angles is 55°. What is the other one (in degrees)?
  13. 13.The two shorter sides of a right-angled triangle are 24 cm and 7 cm. How long is the longest side (in cm)?
  14. 14.In an isosceles triangle, the two equal angles are 32° each. What is the third angle (in degrees)?
  15. 15.The angles of a triangle are in the ratio 1 : 2 : 2. What is the smallest angle (in degrees)?
  16. 16.In triangle ABC, angle A = 28° and angle B = 64°. What is angle C (in degrees)?
  17. 17.In an isosceles triangle, the two equal angles are 61° each. What is the third angle (in degrees)?
  18. 18.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles (in degrees)?
  19. 19.Can a triangle have sides of 21 cm, 8 cm and 11 cm? (a) Yes (b) No
  20. 20.In triangle ABC, angle A = 97° and angle B = 29°. What is angle C (in degrees)?
  21. 21.The angles of a triangle are in the ratio 1 : 2 : 3. What is the biggest angle (in degrees)?
  22. 22.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)?
  23. 23.Can a triangle have sides of 7 cm, 7 cm and 18 cm? (a) Yes (b) No
  24. 24.Can a triangle have sides of 18 cm, 11 cm and 2 cm? (a) No (b) Yes
  25. 25.The angles of a triangle are in the ratio 1 : 2 : 6. What is the biggest angle (in degrees)?
  26. 26.In triangle ABC, angle A = 80° and angle B = 77°. What is angle C (in degrees)?
  27. 27.In an isosceles triangle, the angle between the two equal sides is 144°. What is each of the other two angles (in degrees)?
  28. 28.In a right-angled triangle, one of the other two angles is 65°. What is the third angle (in degrees)?
  29. 29.In a right-angled triangle, one of the other two angles is 40°. What is the third angle (in degrees)?
  30. 30.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)?
  31. 31.An exterior angle of a triangle is 135°. One of its two interior opposite angles is 78°. What is the other one (in degrees)?
  32. 32.The two interior opposite angles of a triangle are 27° and 67°. What is the exterior angle (in degrees)?
  33. 33.In an isosceles triangle, the angle between the two equal sides is 32°. What is each of the other two angles (in degrees)?
  34. 34.Can a triangle have sides of 13 cm, 3 cm and 6 cm? (a) Yes (b) No
  35. 35.An exterior angle of a triangle is 86°. One of its two interior opposite angles is 56°. What is the other one (in degrees)?
  36. 36.The angles of a triangle are in the ratio 1 : 3 : 5. What is the smallest angle (in degrees)?
  37. 37.An exterior angle of a triangle is 81°. One of its two interior opposite angles is 50°. What is the other one (in degrees)?
  38. 38.Can a triangle have sides of 10 cm, 17 cm and 6 cm? (a) No (b) Yes
  39. 39.The two shorter sides of a right-angled triangle are 15 cm and 8 cm. How long is the longest side (in cm)?
  40. 40.The angles of a triangle are in the ratio 1 : 4 : 5. What is the biggest angle (in degrees)?

Answer key

  1. 36
  2. 38
  3. 30
  4. 17
  5. 40
  6. 24
  7. 46
  8. 70
  9. 71
  10. 32
  11. 90
  12. 35
  13. 25
  14. 116
  15. 36
  16. 88
  17. 58
  18. 30
  19. No
  20. 54
  21. 90
  22. 15
  23. No
  24. No
  25. 120
  26. 23
  27. 18
  28. 25
  29. 50
  30. 8
  31. 57
  32. 94
  33. 74
  34. No
  35. 30
  36. 20
  37. 31
  38. No
  39. 17
  40. 90

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