Question

A road sign is in the shape of a regular pentagon. What is the measure of each angle on the sign? Round to the nearest tenth. 540 252 54 Od 108

Answer 1

Internal angles of a polygon

The triangle has n=3 sides, and the sum of its internal angles is 180°

The rectangle has n=4 sides, and the sumo of its internal angles is 360°

There is a general formula to calculate the sum of the internal angles of any polygon of n sides:

Sum = 180° ( n -2 )

For a pentagon (n=5), the sum of angles is:

Sum = 180° ( 5 -2 ) = 180° * 3 = 540°

We are required to find the measure of each internal angle. Since the pentagon is regular, all of its internal angles measure the same, thus:

The measure of each angle = 540° / 5 = 108°