Answer: The value of X is 14
Explanation:
First you need to find the sum of all the interior angles of the polygon using the polygon interior angle sum theorem:
(n - 2) 180°
n = # of angles
Substitute:
(6 - 2) 180
(4) 180
= 720°
Then you can calculate the value of x by setting up an equation adding all of the interior angles and isolating the x variable:
10x + (8x - 16) + (12x - 8) + (7x + 2) + (9x + 4) + (6x + 10) = 720
Add like-terms:
52x + -8 +8 = 720 +8
52/52x = 728/52
x = 14