Answer:
The polygon has 9 sides
Step-by-step explanation:
we know that
A regular polygon has equal length sides and equal interior angles
step 1
Find the measure of the interior angle
Remember that
The interior angle plus the exterior angle must be equal to 180 degrees (form a linear pair)
Let
x ----> the measure of each interior angle in the regular polygon
so
[tex]x+40^o=180^o[/tex]
solve for x
[tex]x=180^o-40^o=140^o[/tex]
step 2
Find the number of sides of the regular polygon
we know that
The measure of each interior angle in a regular polygon is given by the formula
[tex]x=\frac{(n-2)180^o}{n}[/tex]
where
n is the number of sides of the polygon
substitute the given values
[tex]140^o=\frac{(n-2)180^o}{n}[/tex]
solve for n
[tex]140n=180n-360\\180n-140n=360\\40n=360\\n=9\ sides[/tex]
therefore
The polygon has 9 sides
