SOLUTION: if the vertex of a regular polygon is 150 degrees what is the measure of the central angle

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Question 233700: if the vertex of a regular polygon is 150 degrees what is the measure of the central angle
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

All vertex angles (also called "interior angles") of a regular
polygon have equal measures. If this regular polygon has n sides,
then the sum of all the interior angles is 150° times n. The sum
of the measures of all the interior angles of any polygon with n
sides is (n-2) times 180°. So we have this equation

+150n=%28n-2%29%28180%29+

Solve that and we get n=12

So we have a 12-sided regular polygon (a regular dodecagon)



Now we'll connect all the vertices to the center,



There are 12 central angles all
with equal measure and since they
all add up to 360°, each one is 1%2F12
of 360° or 30°.

Edwin