anonymous
  • anonymous
The measure of each interior angle of a regular polygon is 144 degrees. How many sides does the polygon have?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
Regular 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 (n-2)*180 degrees. So\[144n=(n-2)180\rightarrow144n=180n-360\]Solve for n to get
anonymous
  • anonymous
\[360=180n-144n=36n\]Dividing both sides by 36 gives \[n=10\]
anonymous
  • anonymous
You have a decagon.

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anonymous
  • anonymous
thank you

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