# The interior angles of a hexagon are x+2, x-8, x +7, x -3, x+6, and x -4. What is the value of x?

Jun 24, 2018

$x = 120$

#### Explanation:

$\text{the "color(blue)"sum of the interior angles of a polygon}$ is.

•color(white)(x)"sum "=180^@(n-2)

$\text{where n is the number of sides}$

$\text{for a hexagon } n = 6$

$\text{sum } = {180}^{\circ} \times 4 = {720}^{\circ}$

$\text{sum the 6 given angles and equate to 720}$

$x + 2 + x - 8 + x + 7 + x - 3 + x + 6 + x - 4 = 720$

$6 x = 720 \Rightarrow x = \frac{720}{6} = 120$