Answer:
Around 81.87 degrees (rounded)
Explanation:
To find the angle of a sector with a radius of 8cm and a perimeter of 26cm, we use the formula angle = (perimeter of sector / radius) * (180 / π). Plugging in the values we get angle = (26 / 8) * (180 / π) which is approximately 81.87 degrees. We can double-check this answer by using the formula for the arc length of a sector, which gives us a value of approximately 14.77cm. Using the formula for the perimeter of a sector, we can confirm that this is correct. Therefore, the angle of the sector is approximately 81.87 degrees.