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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 154 · 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 20 cm and one of the other sides is 16 cm. How long is the third side (in cm)?
  2. 2.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)?
  3. 3.An exterior angle of a triangle is 120°. One of its two interior opposite angles is 80°. What is the other one (in degrees)?
  4. 4.Can a triangle have sides of 11 cm, 10 cm and 19 cm? (a) Yes (b) No
  5. 5.The angles of a triangle are in the ratio 1 : 2 : 6. What is the biggest angle (in degrees)?
  6. 6.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)?
  7. 7.Can a triangle have sides of 8 cm, 5 cm and 16 cm? (a) No (b) Yes
  8. 8.The angles of a triangle are in the ratio 1 : 1 : 2. What is the smallest angle (in degrees)?
  9. 9.Can a triangle have sides of 6 cm, 6 cm and 3 cm? (a) Yes (b) No
  10. 10.Can a triangle have sides of 9 cm, 9 cm and 16 cm? (a) No (b) Yes
  11. 11.The two shorter sides of a right-angled triangle are 24 cm and 7 cm. How long is the longest side (in cm)?
  12. 12.In triangle ABC, angle A = 30° and angle B = 63°. What is angle C (in degrees)?
  13. 13.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles (in degrees)?
  14. 14.An exterior angle of a triangle is 75°. One of its two interior opposite angles is 41°. What is the other one (in degrees)?
  15. 15.In triangle ABC, angle A = 60° and angle B = 69°. What is angle C (in degrees)?
  16. 16.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles (in degrees)?
  17. 17.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)?
  18. 18.In a right-angled triangle, one of the other two angles is 12°. What is the third angle (in degrees)?
  19. 19.Can a triangle have sides of 8 cm, 12 cm and 5 cm? (a) No (b) Yes
  20. 20.The two shorter sides of a right-angled triangle are 10 cm and 24 cm. How long is the longest side (in cm)?
  21. 21.The two interior opposite angles of a triangle are 72° and 56°. What is the exterior 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.The two interior opposite angles of a triangle are 56° and 48°. What is the exterior angle (in degrees)?
  24. 24.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles (in degrees)?
  25. 25.The two interior opposite angles of a triangle are 32° and 58°. What is the exterior angle (in degrees)?
  26. 26.In an isosceles triangle, the two equal angles are 23° each. What is the third angle (in degrees)?
  27. 27.The two shorter sides of a right-angled triangle are 7 cm and 24 cm. How long is the longest side (in cm)?
  28. 28.In triangle ABC, angle A = 31° and angle B = 57°. What is angle C (in degrees)?
  29. 29.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles (in degrees)?
  30. 30.In an isosceles triangle, the two equal angles are 83° each. What is the third angle (in degrees)?
  31. 31.In a right-angled triangle, one of the other two angles is 80°. What is the third angle (in degrees)?
  32. 32.Can a triangle have sides of 17 cm, 5 cm and 11 cm? (a) Yes (b) No
  33. 33.The angles of a triangle are in the ratio 3 : 5 : 7. What is the biggest angle (in degrees)?
  34. 34.The two interior opposite angles of a triangle are 79° and 79°. What is the exterior angle (in degrees)?
  35. 35.In a right-angled triangle, one of the other two angles is 64°. What is the third angle (in degrees)?
  36. 36.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)?
  37. 37.In a right-angled triangle, one of the other two angles is 43°. What is the third angle (in degrees)?
  38. 38.In triangle ABC, angle A = 47° and angle B = 78°. What is angle C (in degrees)?
  39. 39.In an isosceles triangle, the two equal angles are 73° each. What is the third angle (in degrees)?
  40. 40.The two shorter sides of a right-angled triangle are 5 cm and 12 cm. How long is the longest side (in cm)?

Answer key

  1. 12
  2. 4
  3. 40
  4. Yes
  5. 120
  6. 15
  7. No
  8. 45
  9. Yes
  10. Yes
  11. 25
  12. 87
  13. 35
  14. 34
  15. 51
  16. 30
  17. 16
  18. 78
  19. Yes
  20. 26
  21. 128
  22. 17
  23. 104
  24. 20
  25. 90
  26. 134
  27. 25
  28. 92
  29. 70
  30. 14
  31. 10
  32. No
  33. 84
  34. 158
  35. 26
  36. 7
  37. 47
  38. 55
  39. 34
  40. 13

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