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.