If the figure below is a regular polygon, find the value of x.

For the given figure the value of x is 14

Given  a regular polygon

A regular polygon is a polygon which has all sides equal and each side  subtends equal interior angle at the center.

According to the figure

We are given a regular polygon with 10 sides

The angle subtended  at the center is given as

(10x + 4)°

The Sum of interior angles =  ( 10-2) = 1440°

So the angle subtended by one side at the center is given as follows

1440°/ 10 = 144°

Since the angle subtended at the center = 144° = (10x + 4)°

so by solving this we can get

140 = 10x

x = 14  

For more information please refer to the link below

link

Sum of the interior angles of a regular polygon is given by = (n-2)180°

where n is the no. of sides.

In the above figure, n= 10

Therefore, sum of the interior angles = (10-2)×180°

= 8×180°

= 1440°

Measure of each angle = 1440/10= 144°

Therefore, 10x+4=144

=> 10x= 140

=> x= 14

the monthly balance will be $75,000