Question

If the polygon shown below is a regular nonagon,what is the value of x

Answer 1

`x=40^o`

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

`((n-2)180^o)/(n)`

where

n is the number of sides

In this problem we have

n=9 sides

substitute

`((9-2)180^o)/(9)=140^o`

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

`x+140^o=180^o`

solve for x

`x=180^o-140^o=40^o`