SOLUTION: The measure of one interior angle of a regular polygon is 144 degrees find the number of sides of the polygon?
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Question 181166: The measure of one interior angle of a regular polygon is 144 degrees find the number of sides of the polygon?
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The measure of one interior angle of a regular polygon is 144 degrees find the number of sides of the polygon?
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The corresponding exterior angle is 36 degrees.
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The sum of the exterior angles is always 360.
Equation:
# of exterior angles = 360/36 = 10
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Therefore the number of sides is 10.
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Cheers,
Stan H.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The sum of the measures of the interior angles of any polygon is )
where n is the number of sides. Therefore, the measure of one of the interior angles of a regular polygon is this sum divided by the number of interior angles in the polygon which is always identical to the number of sides of the polygon.
}{n} = 144 \ \ \Rightarrow \ \ 180n - 360 = 144n \ \ \Rightarrow \ \ 36n = 360 \ \ \Rightarrow \ \ n = 10)
John
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