Answer :
We have a circular sector, with radius 6 and an area of 6*pi square units:
We have to calculate the value of the angle.
We can use the fact that we have a fraction of the circle. We can calculate what fraction of the circle it represents by dividing the area of the sector by the area of the circle:
[tex]\frac{A}{A_c}=\frac{6\pi}{\pi r^2}=\frac{6\pi}{6^2\pi}=\frac{1}{6}[/tex]We know that our sector is 1/6 of the circle.
Then, the angle is 1/6 of the total angle of the circle, which, in degrees, is 360 deg.
Then, we can calculate our angle multiplying 1/6 by 360:
[tex]\alpha=\frac{1}{6}\cdot360=60[/tex]The measure is 60 degrees.
