Question

A regular hexagon is shown below.

Which statement explains why the equation 4x+40=6x can be used to solve for x?

All polygons have congruent angles.

The interior angles of a regular hexagon are congruent.

The sum of the angle measures of a hexagon is 720º.

The value of 6 x equals the sum of the angles of a regular hexagon.

Answer 1

The interior angles of a regular hexagon are congruent

Explanation:

we know that

A regular polygon is a polygon that all interior angles are equal in measure, and all sides have the same length.

The sum of the measure of the interior angles in a regular polygon is equal to

`S=(n-2)180^o`

where

n is the number of sides

For n=6 (hexagon)

`S=(6-2)180^o\\S=720^o`

Divide by the number of sides

`(720^o)/(6)=120^o`

In this problem we have

`(4x+40)^o=6x^o`

solve for x

`6x-4x=40\\2x=40\\x=20^o`

Verify the measure of the interior angle in a regular hexagon with the value of x

`(4(20)+40)^o=120^o` ---> is ok

`6(20)=120^o` ---> is ok

therefore

The interior angles of a regular hexagon are congruent