SOLUTION: Given the following measures of a vertex angle of a regular polygon,determine how many sides it has. A.150 B.156 C.174 D.178

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Question 18709: Given the following measures of a vertex angle of a regular polygon,determine how many sides it has.
A.150 B.156 C.174 D.178
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You can start with the formula for the measure of an interior (vertex) angle of a regular polygon of n sides. A+=+%28%28n-2%29180%29%2Fn
A.
150+=+%28%28n-2%29180%29%2Fn Multiply both sides by n.
150n+=+180n+-+360 Add 360 to both sides.
150n+%2B+360+=+180n Subtract 150n from both sides.
360+=+30n Divide both sides by 30.
n+=+12 The regular polygon has twelve sides.
B. Similarly:
156+=+%28%28n-2%29180%29%2Fn Multiply both sides by n.
156n+=+180n+-+360 Add 360 to both sides.
156n+%2B+360+=+180n Subtract 156n from both sides.
360+=+24n Divide both sides by 24.
n+=+15 The regular polygon has fifteen sides.
C. and D. Follow the same procedure as for A. and B.