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The logo of a certain corporation is in the shape of a polygon, where all angles of a the polygon have equal measures. In the above figure V is one vertex of the polygon. If Y in degrees is the measure of an angle of the polygon and y=5x how many sides does the polygon have?
Option D is the correct answer.
From the figure,
x + y = 180
6*x = 180
x = 30, y = 150
Let number of sides be “n”, hence number of interior angles is also “n”
Sum of all interior angles = 150*n
Formula for sum of interior angles
= 180*(n-2) 180*(n-2) = 150*n
30*n = 360
n = 360/30 = 12