Question

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.

Answer 1

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 °

Answer 2

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