EXAMPLE 1 Identifying Figures

It is not a polygon. The bottom edge does not have line segments.

a. It is a regular polygon. Its angles have equal measures, and its sides have equal lengths.

b.

Is the bottom of the box a polygon, a regular polygon, or not a polygon? Explain.

SOLUTION

EXAMPLE 2 Finding an Angle Measure

A regular octagon has 8 sides, so n = 8.o

(n – 2) 180n

=o

(8 – 2) 1808

=8

1080o

= 135o

Substitute 8 for n.

Simplify numerator.

Divide.

The measure of one angle in a regular octagon is 135.

ANSWERo

Find the measure of one angle in a regular octagon.

GUIDED PRACTICE for Examples 1 and 2

1. Find the sum of the angle measures in a 9-gon.

ANSWER

The sum of angle measures in a 9-gon is 1260 .o

GUIDED PRACTICE for Examples 1 and 2

2. Find the measure of one angle in a regular heptagon. Round to the nearest tenth of a degree.

ANSWER

The measure of one angle in a regular heptagon is 128.6 .

o