SOLUTION: How many sides has a regular polygon whose interior angle is 22½
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Question 1179357: How many sides has a regular polygon whose interior angle is 22½
Found 3 solutions by ankor@dixie-net.com, MathLover1, ikleyn:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
How many sides has a regular polygon whose interior angle is 22½
:
= 16 sides
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Since an interior angle is degrees, its adjacent exterior angle is degrees.
Exterior angles of any polygon always add up to degrees. With the polygon being regular, we can just divide by to get the number of sides .
so, there is a regular polygon whose interior angle is °
double check this way:
Let be the number of sides of a regular polygon whose interior angles are each °.
Then °.
=>
so, there is a regular polygon whose interior angle is °
Thus, ° cannot be an angle of a regular polygon.
Answer by ikleyn(52805) (Show Source): You can put this solution on YOUR website!
.
How many sides has a regular polygon whose interior angle is 22½
~~~~~~~~~~~~~
Having two different answers that contradict each other, may PERPLEX you.
So I came to make things clear to you.
Your problem in the post is posed INCORRECTLY.
There is no a regular polygon with the interior angle of 22 1/2 degrees.
If the EXTERIOR angle of a regular polygon is 22 1/2 degrees,
then the number of sides (same as the number of vertices) is = 16.
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