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.
a) x = 120
b) x = 9
c) x = 28.5
d) x = 21
In a regular polygon, all the angles are equal, so the measure of each angle is (n-2)*180°/n, where n is the number of sides.
In this case, we are given that one of the angles is 8x - 48.
Setting up an equation, we have:
8x - 48 = (6-2)*180/6
Simplifying the equation, we get:
8x - 48 = 4*180/6
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 get:
x = 168/8
x = 21
Therefore, the value of x is 21.
The correct answer is d) x = 21.