Answer:
[tex]x=165^o[/tex]
Step-by-step explanation:
we know that
The measure of the interior angle in an equilateral triangle is equal to 60 degrees
The measure of the interior angle in a regular octagon is equal to
[tex]\frac{(n-2)180}{n}[/tex]
where
n is the number of sides
In this problem we have
[tex]n=8\ sides[/tex]
substitute
[tex]\frac{(8-2)180}{8}[/tex]
[tex]\frac{(6)180}{8}=135^o[/tex]
we have that, based in the diagram
The sum of the interior angle of the equilateral triangle plus the interior angle of a regular octagon plus the value of x must be equal to 360 degrees (complete circle)
so
[tex]x+60^o+135^o=360^o[/tex]
solve for x
[tex]x+195^o=360^o[/tex]
[tex]x=360^o-195^o[/tex]
[tex]x=165^o[/tex]
