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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 896 · 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 interior opposite angles of a triangle are 76° and 58°. What is the exterior angle (in degrees)?
  2. 2.In a right-angled triangle, one of the other two angles is 21°. What is the third angle (in degrees)?
  3. 3.The angles of a triangle are in the ratio 2 : 3 : 5. What is the biggest angle (in degrees)?
  4. 4.An exterior angle of a triangle is 70°. One of its two interior opposite angles is 22°. What is the other one (in degrees)?
  5. 5.The two interior opposite angles of a triangle are 70° and 59°. What is the exterior angle (in degrees)?
  6. 6.An exterior angle of a triangle is 113°. One of its two interior opposite angles is 57°. What is the other one (in degrees)?
  7. 7.Can a triangle have sides of 3 cm, 1 cm and 3 cm? (a) Yes (b) No
  8. 8.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles (in degrees)?
  9. 9.An exterior angle of a triangle is 147°. One of its two interior opposite angles is 69°. What is the other one (in degrees)?
  10. 10.The angles of a triangle are in the ratio 2 : 7 : 9. What is the smallest angle (in degrees)?
  11. 11.In a right-angled triangle, one of the other two angles is 77°. What is the third angle (in degrees)?
  12. 12.In a right-angled triangle, one of the other two angles is 34°. What is the third angle (in degrees)?
  13. 13.Can a triangle have sides of 20 cm, 6 cm and 9 cm? (a) Yes (b) No
  14. 14.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)?
  15. 15.The angles of a triangle are in the ratio 1 : 1 : 2. What is the smallest angle (in degrees)?
  16. 16.In an isosceles triangle, the angle between the two equal sides is 24°. What is each of the other two angles (in degrees)?
  17. 17.The angles of a triangle are in the ratio 3 : 5 : 7. What is the smallest angle (in degrees)?
  18. 18.The angles of a triangle are in the ratio 2 : 3 : 4. What is the smallest angle (in degrees)?
  19. 19.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)?
  20. 20.Can a triangle have sides of 14 cm, 6 cm and 8 cm? (a) No (b) Yes
  21. 21.The angles of a triangle are in the ratio 2 : 3 : 5. What is the smallest angle (in degrees)?
  22. 22.Can a triangle have sides of 2 cm, 2 cm and 1 cm? (a) Yes (b) No
  23. 23.The two shorter sides of a right-angled triangle are 7 cm and 24 cm. How long is the longest side (in cm)?
  24. 24.The two interior opposite angles of a triangle are 24° and 55°. What is the exterior angle (in degrees)?
  25. 25.An exterior angle of a triangle is 96°. One of its two interior opposite angles is 58°. What is the other one (in degrees)?
  26. 26.In an isosceles triangle, the angle between the two equal sides is 148°. What is each of the other two angles (in degrees)?
  27. 27.The two interior opposite angles of a triangle are 27° and 76°. What is the exterior angle (in degrees)?
  28. 28.The longest side of a right-angled triangle is 13 cm and one of the other sides is 5 cm. How long is the third side (in cm)?
  29. 29.The angles of a triangle are in the ratio 3 : 3 : 4. What is the biggest angle (in degrees)?
  30. 30.Can a triangle have sides of 9 cm, 3 cm and 10 cm? (a) Yes (b) No
  31. 31.In an isosceles triangle, the angle between the two equal sides is 56°. What is each of the other two angles (in degrees)?
  32. 32.In triangle ABC, angle A = 50° and angle B = 94°. What is angle C (in degrees)?
  33. 33.In triangle ABC, angle A = 74° and angle B = 81°. What is angle C (in degrees)?
  34. 34.In a right-angled triangle, one of the other two angles is 46°. What is the third angle (in degrees)?
  35. 35.Can a triangle have sides of 17 cm, 8 cm and 6 cm? (a) No (b) Yes
  36. 36.In triangle ABC, angle A = 35° and angle B = 36°. What is angle C (in degrees)?
  37. 37.The two interior opposite angles of a triangle are 67° and 29°. What is the exterior angle (in degrees)?
  38. 38.An exterior angle of a triangle is 62°. One of its two interior opposite angles is 37°. What is the other one (in degrees)?
  39. 39.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles (in degrees)?
  40. 40.In a right-angled triangle, one of the other two angles is 15°. What is the third angle (in degrees)?

Answer key

  1. 134
  2. 69
  3. 90
  4. 48
  5. 129
  6. 56
  7. Yes
  8. 55
  9. 78
  10. 20
  11. 13
  12. 56
  13. No
  14. 24
  15. 45
  16. 78
  17. 36
  18. 40
  19. 8
  20. No
  21. 36
  22. Yes
  23. 25
  24. 79
  25. 38
  26. 16
  27. 103
  28. 12
  29. 72
  30. Yes
  31. 62
  32. 36
  33. 25
  34. 44
  35. No
  36. 109
  37. 96
  38. 25
  39. 75
  40. 75

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