NandishSS wrote: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?
A 5
B 6
C 10
D 12
E 30
Since y and x form a straight line, y+x = 180.
Substituting y=5x into y+x=180, we get:
5x+x = 180
6x = 180
x = 30, implying that y = 5*30 = 150.
The sum of the angles inside a polygon = (n-2)(180), where n is the number of sides and the number of angles.
If all the angles are equal, then the measure of each angle = (sum of the angles)/(number of angles) = [(n-2)(180)]/n.
Since the measure of each angle in the logo = 150, we get:
[(n-2)(180)]/n = 150
180n - 360 = 150n
30n = 360
n = 12.
The correct answer is
D.
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