The measures of all angles in a regular octagon are (4x + 12)°. how would you find the value of x?
The sum of the interior angles of an n-gon is
180(n-2)
so here n=8.
Find the sum and then set it equal to 4x+12
solve for x
d is between ce=6x cd=4x+8 de=7 units find ce
To find the value of x in the equation (4x + 12)° for a regular octagon, we can use the property that the sum of all the interior angles of a polygon with n sides is equal to (n-2) * 180 degrees.
In the case of an octagon (a polygon with 8 sides), the sum of the interior angles is (8-2) * 180 = 6 * 180 = 1080 degrees.
Since we are given that each angle in the regular octagon is (4x + 12)°, we can write the equation:
8 * (4x + 12) = 1080
Simplifying the equation:
32x + 96 = 1080
32x = 1080 - 96
32x = 984
x = 984 / 32
x ≈ 30.75
Therefore, the value of x is approximately 30.75.