Answer:
[tex]x=40^o[/tex]
Step-by-step explanation:
the picture of the question in the attached figure
step 1
Find the measure of the interior angle of a regular nonagon
The formula to calculate the measure of the interior angle in any polygon is given by
[tex]\frac{(n-2)180^o}{n}[/tex]
where
n is the number of sides
In this problem we have
n=9 sides
substitute
[tex]\frac{(9-2)180^o}{9}=140^o[/tex]
step 2
Find the value of x
Remember that
The sum of the interior angle and the exterior angle in any vertex of the polygon must be equal to 180 degrees
so
[tex]x+140^o=180^o[/tex]
solve for x
[tex]x=180^o-140^o=40^o[/tex]
