Find the number of sides of a regular polygon if the measure of an interior angle is 157.5°

In a polygon with n sides, the sum of the measures of the interior angles, S, is

In a regular polygon with n sides, the measure of each interior angle, a, is the sum of the measures of the interior angles divided by the number of sides, or

In this case, we know the measure of one angle, a = 157.5°, so we plug it into the second formula and solve for n.

The polygon has 16 sides.

step-by-step explanation:

let x and 400 - x be the two numbers.  

==> 0.80x + 0.85(400 - x) = 400 - 68 from the statement of the problem.  

< ==> 0.80x + 0.85(400 - x) = 400 - 68  

==> 340 - 0.05x = 332  

< ==> -0.05x = -8 ==> x = 160, the first number ==> 400 - x = 240, the second number.