A school is designed so that 5 hallways meet at the library in the shape of a regular pentagon. Find the measure of one of the interior angles of the pentagon.

Question

mathstudent55 · Answer

|dw:1356935867603:dw|

mathstudent55 · Answer

In this case, n = 5 = number of sides

anonymous · Answer

wait how would u show ur work

mathstudent55 · Answer

All you need to do is show two things.
In a regular polygon, all angles are congruent. That means all their measures are the same.
Also, in any polygon, the sum of the measures of the interior angles of a polygon is
(n - 2)180, where n = number of sides.
Since a pentagon has 5 sides, the sum of measures of the interior angles is
(5 - 2)180 = 3(180) = 540
Since all angles are congruent, each angle is 540/5