The measure of a single angle in a regular octagon is (4x + 12) Á. Find the value of x. Show equations and all work that leads to your answer.

The sum, S, of the internal angles of regular polygon is (n-2) 180°

Where n is the number of sides.

For the octagon n = 8, then S (8 - 2) 180° = 1080°.

Given that it is regular, each angle is 1080° / 8 = 135°

Then 4x + 12 = 135 = > 4x = 135 - 12 = 123

x = 123 / 4 = 30.75 °

4x+12=135 8 (4x+12) = 8*135=1080

-12 - 12 32x+96=1080

4x=123 - 96 - 96

/4 / 4 32x=984

x=30.75 / 32 / 32

x=30.75