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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 200 · 40 sums
TalentJR

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.In a right-angled triangle, one of the other two angles is 35°. What is the third angle (in degrees)?
  2. 2.The two shorter sides of a right-angled triangle are 8 cm and 15 cm. How long is the longest side (in cm)?
  3. 3.An exterior angle of a triangle is 111°. One of its two interior opposite angles is 63°. What is the other one (in degrees)?
  4. 4.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles (in degrees)?
  5. 5.In an isosceles triangle, the angle between the two equal sides is 108°. What is each of the other two angles (in degrees)?
  6. 6.The angles of a triangle are in the ratio 1 : 2 : 6. What is the smallest angle (in degrees)?
  7. 7.In an isosceles triangle, the two equal angles are 45° each. What is the third angle (in degrees)?
  8. 8.The two interior opposite angles of a triangle are 73° and 67°. What is the exterior angle (in degrees)?
  9. 9.The two interior opposite angles of a triangle are 36° and 74°. What is the exterior angle (in degrees)?
  10. 10.In a right-angled triangle, one of the other two angles is 31°. What is the third angle (in degrees)?
  11. 11.In a right-angled triangle, one of the other two angles is 69°. What is the third angle (in degrees)?
  12. 12.In triangle ABC, angle A = 86° and angle B = 54°. What is angle C (in degrees)?
  13. 13.In an isosceles triangle, the two equal angles are 57° each. What is the third angle (in degrees)?
  14. 14.In an isosceles triangle, the two equal angles are 71° each. What is the third angle (in degrees)?
  15. 15.In a right-angled triangle, one of the other two angles is 27°. What is the third angle (in degrees)?
  16. 16.The longest side of a right-angled triangle is 39 cm and one of the other sides is 36 cm. How long is the third side (in cm)?
  17. 17.Can a triangle have sides of 11 cm, 19 cm and 6 cm? (a) Yes (b) No
  18. 18.In an isosceles triangle, the angle between the two equal sides is 58°. What is each of the other two angles (in degrees)?
  19. 19.The angles of a triangle are in the ratio 2 : 3 : 5. What is the biggest angle (in degrees)?
  20. 20.Can a triangle have sides of 9 cm, 10 cm and 22 cm? (a) Yes (b) No
  21. 21.In triangle ABC, angle A = 90° and angle B = 27°. What is angle C (in degrees)?
  22. 22.Can a triangle have sides of 9 cm, 8 cm and 18 cm? (a) No (b) Yes
  23. 23.The two shorter sides of a right-angled triangle are 36 cm and 15 cm. How long is the longest side (in cm)?
  24. 24.Can a triangle have sides of 7 cm, 15 cm and 4 cm? (a) No (b) Yes
  25. 25.The two shorter sides of a right-angled triangle are 7 cm and 24 cm. How long is the longest side (in cm)?
  26. 26.The two interior opposite angles of a triangle are 53° and 40°. What is the exterior angle (in degrees)?
  27. 27.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)?
  28. 28.Can a triangle have sides of 25 cm, 12 cm and 9 cm? (a) No (b) Yes
  29. 29.The angles of a triangle are in the ratio 2 : 7 : 9. What is the biggest angle (in degrees)?
  30. 30.The angles of a triangle are in the ratio 1 : 2 : 3. What is the biggest angle (in degrees)?
  31. 31.In triangle ABC, angle A = 53° and angle B = 77°. What is angle C (in degrees)?
  32. 32.In triangle ABC, angle A = 57° and angle B = 24°. What is angle C (in degrees)?
  33. 33.The longest side of a right-angled triangle is 5 cm and one of the other sides is 3 cm. How long is the third side (in cm)?
  34. 34.In triangle ABC, angle A = 96° and angle B = 55°. What is angle C (in degrees)?
  35. 35.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)?
  36. 36.An exterior angle of a triangle is 113°. One of its two interior opposite angles is 33°. What is the other one (in degrees)?
  37. 37.In an isosceles triangle, the two equal angles are 52° each. What is the third angle (in degrees)?
  38. 38.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)?
  39. 39.In an isosceles triangle, the two equal angles are 64° each. What is the third angle (in degrees)?
  40. 40.In triangle ABC, angle A = 80° and angle B = 54°. What is angle C (in degrees)?

Answer key

  1. 55
  2. 17
  3. 48
  4. 30
  5. 36
  6. 20
  7. 90
  8. 140
  9. 110
  10. 59
  11. 21
  12. 40
  13. 66
  14. 38
  15. 63
  16. 15
  17. No
  18. 61
  19. 90
  20. No
  21. 63
  22. No
  23. 39
  24. No
  25. 25
  26. 93
  27. 8
  28. No
  29. 90
  30. 90
  31. 50
  32. 99
  33. 4
  34. 29
  35. 16
  36. 80
  37. 76
  38. 15
  39. 52
  40. 46

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