Number of sides in a polygon

Question

All but one of the interior angles of a convex polygon measure 163. How many sides could the polygon have?

Please help me understand this. Thanks.

Answer 1

Convex polygon measure is 163.

Sum of the interior angles of a convex polygon is ( n - 2 ) * 180 = measure of an angle.

One angle of a convex polygon =

Let the measure of an angle be represented by A.

= A

( n - 2 ) * 180 = A * n

180 n - 360 = An

180n - An = 360

180 n - An = 360

n ( 180 - A ) = 360

Where n=number of sides and A is the measure of an angle.

So n = 360/( 180 - 163)

= 360/17 = 21.176

Convex polygon with 21 sides.