document.write( "Question 954797: Determine if it is possible for a regular polygon to have an interior angle with the given angle measures. Explain you reasoning.
\n" ); document.write( "a.165 b.171 c.75 d.40
\n" ); document.write( "Please show the work. \n" ); document.write( "

Algebra.Com's Answer #583194 by Fombitz(32388) $\"\"$ $\"About$

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Interior angles for a polygon follow the formula,
\n" ); document.write( " $\"A=180%28n-2%29%2Fn\"$
\n" ); document.write( "a) $\"180%28n-2%29=165n\"$
\n" ); document.write( " $\"180n-360=165n\"$
\n" ); document.write( " $\"15n=360\"$
\n" ); document.write( " $\"n=24\"$
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\n" ); document.write( "b) $\"180%28n-2%29=171n\"$
\n" ); document.write( " $\"180n-360=171n\"$
\n" ); document.write( " $\"9n=360\"$
\n" ); document.write( " $\"n=40\"$
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\n" ); document.write( "c) $\"180%28n-2%29=75n\"$
\n" ); document.write( " $\"180n-360=75n\"$
\n" ); document.write( " $\"105n=360\"$
\n" ); document.write( " $\"n=24%2F7\"$ <--- Not an integer
\n" ); document.write( "You could have also guessed that since a triangle (3 sides) has an interior angle of 60 and a square (4 sides) has an interior of 90, a value between 60 and 90 would not work.
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\n" ); document.write( "d) $\"180n-360=40n\"$
\n" ); document.write( " $\"180n-360=40n\"$
\n" ); document.write( " $\"140n=360\"$
\n" ); document.write( " $\"n=18%2F7\"$ <--- Not an integer
\n" ); document.write( "You could have also guessed since a triangle has the fewest sides and it's interior angle is 60. So any angle less than 60 would not work.
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\n" ); document.write( "Only a and b are valid interior angles.
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