A convex polygon has n sides An angle measures S2n5 if S su

A convex polygon has n sides. An angle measures S/(2n-5), if S = sum of all the other angles of polygon. What is the measure of the angle?

The sum of the interior angles of a convex polygon is equal to (n - 2)*180 where n is the number of sides.

The convex polygon in the problem has n sides. One angle is S/(2n - 5) and the the sum of the others is S.

We have to determine S/(2n - 5)

S/(2n - 5) + S = (n - 2)*180

=> S + S(2n - 5) = (n - 2)(2n - 5)*180

=> S + 2nS - 5S = (n - 2)(2n - 5)*180

=> -4S + 2nS = (n - 2)(2n - 5)*180

=> S = (n - 2)(2n - 5)*180/(2n - 4)

=> S = (2n - 5)*90

=> S/(2n - 5) = 90

The measure of the angle is 90 degrees