SOLUTION: An interior angle of a regular convex polygon measures 144 degress how many sides does the polygon have?

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Question 284065: An interior angle of a regular convex polygon measures 144 degress how many sides does the polygon have?
Found 2 solutions by solver91311, Earlsdon:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The measure of an interior angle of a regular convex polygon can be determined by the following formula:



Doing a little algebra:







You were given an IA of 144 degrees, so do the math ... so to speak.

John

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The measure of an interior angle (A) of a regular polygon of n sides is given by:
A+=+%28n-2%29%2A180%2Fn To find n, substitute A = 144 and solve.
144+=+%28%28n-2%29%2A180%29%2Fn Multiply both sides by n and simplify the right side.
144n+=+180n-360 Subtract 144n from both sides.
0+=+36n-360 Add 360 to both sides.
360+=+36n Finally, divide both sides by 36.
highlight%2810+=+n%29
The regular polygon has 10 sides.