Question

What is the name of the regular polygon that measures 140ﾟ

Answer 1

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

$n(a)=(n-2)180\°$

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

$a=140\°$

substitute in the formula and solve for n

$n(140\°)=(n-2)180\°$

$140n=180n-360$

$180n-140n=360$

$40n=360$

$n=9\ sides$

so

The regular polygon has 9 sides

therefore

The regular polygon is a nonagon