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

Answer:

The interior angles of a regular hexagon are congruent

Step-by-step 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

$\frac{720^o}{6}=120^o$

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