Answer:
The regular polygon is a nonagon
Step-by-step explanation:
The correct question is
What is the name of the regular polygon that each interior angle measures 140ﾟ?
we know that
The formula to find the sum of the interior angles in a regular polygon is equal to
[tex]n(a)=(n-2)180\°[/tex]
where
n is the number of sides of the regular polygon
a is the measure of each interior angle of the regular polygon
we have
[tex]a=140\°[/tex]
substitute in the formula and solve for n
[tex]n(140\°)=(n-2)180\°[/tex]
[tex]140n=180n-360[/tex]
[tex]180n-140n=360[/tex]
[tex]40n=360[/tex]
[tex]n=9\ sides[/tex]
so
The regular polygon has 9 sides
therefore
The regular polygon is a nonagon
