A regular polygon is shown, with the measure of one of its angles labeled 8x − 48.
6 sided regular polygon with one angle labeled 8 times x minus 48
Determine the value of x.
x = 120
x = 9
x = 28.5
x = 21
To find the value of x, we can set the given angle measure equal to the formula for the measure of an angle in a regular polygon: 180(n-2)/n, where n is the number of sides of the polygon.
So, we have:
8x - 48 = 180(6-2)/6
8x - 48 = 180(4)/6
8x - 48 = 720/6
8x - 48 = 120
Adding 48 to both sides, we get:
8x = 120 + 48
8x = 168
Dividing both sides by 8, we find:
x = 168/8
x = 21
Therefore, the value of x is 21.