Question 1179357

Since an interior angle is {{{22&1/2=22.5}}} degrees, its adjacent exterior angle is {{{180-22.5= 157.5}}} degrees. 

Exterior angles of any polygon always add up to {{{360}}} degrees. With the polygon being regular, we can just divide {{{360 }}}by {{{157.5}}} to get the number of sides {{{n}}}.

{{{n=360/157.5=2.2857142857142856}}}

so, there is {{{no}}} a regular polygon whose interior angle is {{{22&1/2}}}° 


double check this way:

Let {{{n}}} be the number of sides of a regular polygon whose interior angles are each {{{22.5}}}°.

Then {{{((n-2)/n)*180 = 22.5}}}°.

{{{(n-2)180= 22.5n}}}

{{{180n-360= 22.5n}}}

{{{180n-22.5n= 360}}}

{{{157.5n= 360}}}

{{{n= 360/157.5}}}

{{{n= 2.2857142857142856}}}=>

so, there is {{{no}}} a regular polygon whose interior angle is {{{22&1/2}}}° 

Thus, {{{22&1/2}}}° cannot be an {{{interior}}} angle of a regular polygon.