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anonymous
 5 years ago
The measure of each interior angle of a regular polygon is 144 degrees. How many sides does the polygon have?
anonymous
 5 years ago
The measure of each interior angle of a regular polygon is 144 degrees. How many sides does the polygon have?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Regular polygon is by DEFINITION a convex polygon that has ALL internal angles and ALL sides equal. You only need the fact that all internal angles are equal. I said in another answer that the sum of the internal angles of ANY convex polygon is (n2)*180 degrees. So\[144n=(n2)180\rightarrow144n=180n360\]Solve for n to get

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[360=180n144n=36n\]Dividing both sides by 36 gives \[n=10\]
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