Formula to find the arc length is:
[tex] s=\frac{\theta}{360} 2\pi r [/tex]
So, if we want to measure the central angle then it will be:
[tex] \theta= \frac{360s}{2r\pi} [/tex]
Where, s= arc length,
r = radius of the circle
[tex] \theta [/tex]= central angle in degrees.
According to the given problem, [tex] s=\frac{1}{2} \pi [/tex] and r = 2.
So, first step is to plug in these values in the above formula.
[tex] \theta=\frac{360*\frac{1}{2}\pi}{2*2\pi} [/tex]
[tex] =\frac{360*\frac{1}{2}}{2*2} [/tex]
π has been cancel out from both top and bottom.
[tex] =\frac{180}{4} [/tex]
=45
So, measure of central angle is 45°.
