Given the regular polygon. Find the measure of each numbered angle.
M<1= 30
M<2= 15
M<3= 75
Show work
We can first determine the total number of angles in the regular polygon using the formula:
180(n-2) where n is the number of sides
We know that all angles in a regular polygon have the same measure, so we can set up an equation using the measure of one angle (x):
30 + 15 + 75 + (n-4)x = 180(n-2)
Simplifying and solving for x, we get:
120 + (n-4)x = 180n - 360
(n-4)x = 60n - 480
x = (60n - 480)/(n-4)
Since x represents the measure of each angle, we can substitute in the number of sides to find its value for this specific regular polygon:
x = (60(3) - 480)/(3-4) = 120
Therefore, each angle in this regular polygon measures 120 degrees.