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

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

Answer 2

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 °