SOLUTION: Q1- THE SUM OF ALL INTERIOR ANGLES OF A REGULAR POLYGON IS 1080 WHAT IS THE MEASURE OF EACH OF ITS EXTERIOR ANGLES?''.

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Q1- THE SUM OF ALL INTERIOR ANGLES OF A REGULAR POLYGON IS 1080 WHAT IS THE MEASURE OF EACH OF ITS EXTERIOR ANGLES?''.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 755901: Q1- THE SUM OF ALL INTERIOR ANGLES OF A REGULAR POLYGON IS 1080 WHAT IS THE MEASURE OF EACH OF ITS EXTERIOR ANGLES?''.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Theorem: The sum of the interior angles in a polygon with n sides is 180%28n-2%29
if the sum of the interior angles is 1080, then
180%28n+-2%29=1080
%28n+-2%29=1080%2F180
n+-2=6
n+=6%2B2
n+=8....we have an octagon
Since each interior angle has the same measure, we divide by 8 to find the measure of one interior angle:
1080%2F8=135
Subtract the measurement of each interior angle from 180 to get the measurement of the corresponding exterior angle.
the corresponding exterior angle is: 180-135=45