we know that
One interior angle of a polygon is found by the equation:
A=(n-2)*180/n
where
A-----> interior angle of a polygon
n-----> the number of sides of the polygon
in this problem
A=157.5°
A=(n-2)*180/n-----> A*n=180*n-360----> 180*n-A*n=360
n*[180-A]=360
n=360/[180-A]-----> n=360/[180-157.5]----> n=16
the answer is
the number of sides is 16
