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

Each INTERNAL angle of a regular octagon is 135 degrees.

If 4x + 12 = 135, then

4x = 123

Divide both sides of the equation by 4.

To find the value of x, we need to use the fact that the sum of the interior angles of any polygon can be found using the formula:

Sum of interior angles = (n - 2) * 180°

Where n is the number of sides of the polygon. In this case, we have a regular octagon, which has 8 sides.

So, the sum of interior angles of our octagon is:

(8 - 2) * 180° = 6 * 180° = 1080°

In a regular octagon, all the angles are congruent, meaning they have the same measure. If the measure of a single angle is given as (4x + 12)°, we can set up an equation:

(4x + 12) * 8 = 1080

Let's solve for x step by step:

1. Distribute 8 to the expression inside the parentheses:

32x + 96 = 1080

2. Subtract 96 from both sides to isolate the variable term:

32x = 1080 - 96
32x = 984

3. Divide both sides by 32 to solve for x:

x = 984 / 32
x = 30.75

So, the value of x is approximately 30.75.