Answer :
Answer:
7 of the angles measure 144 degrees each and one angle measures 72 degrees
Step-by-step explanation:
Let
x -----> represent the measures of the seven same-size angles,
x/2 ----> represent the measure of the one that is "two times smaller."
we know that
The sum of internal angles of a polygon can be calculated as:
[tex]S=180^o(n-2)[/tex]
where
n is the number of sides of the polygon
In this case
n=8 (octagon)
substitute
[tex]S=180^o(8-2)=1,080^o[/tex]
so
The linear equation that represent this problem is
[tex]\frac{x}{2}+7x=1,080[/tex]
solve for x
[tex]\frac{15x}{2}=1,080\\\\15x=2,160\\\\x=144^o[/tex]
so
[tex]\frac{x}{2}=72^o[/tex]
therefore
7 of the angles measure 144 degrees each and one angle measures 72 degrees