Question 945903


 Solution:

1) Find the measure of {{{one}}} {{{interior}}} angle
2) From that, find the measure of one {{{exterior}}} angle
3) Multiply that by {{{8}}}
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1.

Find the measure of one interior angle

By memorization, the formula for the measure of an interior angle in a regular polygon of {{{n}}} sides is

{{{( n -2 )*180 / n}}}

In an octagon, {{{n = 8}}}, so the formula is

{{{( 8 -2 )*180 / 8}}}

{{{6*180 / 8}}}

{{{135}}}º <-- the measure of each {{{interior}}} angle

2.
Find the measure of one {{{exterior}}} angle

Interior and exterior angles are {{{supplements}}}, so the exterior angles are each
{{{180 - 135 = 45}}}º


3.
Finding the sum of them all:

There are eight of these angles, so their sum is

{{{8*45 = 360}}}º



Answer: 

The sum of the measures of the {{{exterior}}} angles of a regular octagon is {{{360}}}º.