given the interior angle of the regular polygon as 157.5 degrees
to solve this,
we subtract the interior angle angle from 180, divide the result into 360 to get the number of sides
so,
lets use this formular
180(n-2) = 157.5n
opening the bracket
180n - 360 = 157.5n
collecting like times
180n - 157.5n = 360
22.5n = 360
divide both sides by 22.5
22.5n/22.5 = 360/22.5
n = 16
therefore, the polygon has 16 sides