What is the measure for a Single angle in a regular octagon is (4X +12° )?

find the value of X

https://www.mathsisfun.com/geometry/interior-angles-polygons.html

4X +12° = 135
4x = 123
x = 30.75

To find the value of X in the given equation, we need to use the information that the measure of a single angle in a regular octagon is given by (4X + 12°).

In a regular octagon, each interior angle is equal. Since an octagon has 8 angles, we can say that the sum of all the interior angles of an octagon is equal to 8 times the measure of a single angle.

So, the sum of the interior angles of the octagon = 8 × (4X + 12°).

Now, we know that the sum of the interior angles of a regular octagon is given by the formula (n - 2) × 180°, where n is the number of sides of the polygon.

Substitute n = 8 into the formula: (8 - 2) × 180° = 6 × 180° = 1080°.

Now, equate the two expressions for the sum of the interior angles and solve for X:

8 × (4X + 12°) = 1080°.

Simplify the equation by distributing 8 on the left side:

32X + 96° = 1080°.

Next, isolate X by moving the constant term to the right side:

32X = 1080° - 96°.

32X = 984°.

Finally, divide both sides by 32 to solve for X:

X = 984° / 32.

X ≈ 30.75°.

Therefore, the value of X is approximately 30.75° in the given equation.