Question 954797
Interior angles for a polygon follow the formula,
{{{A=180(n-2)/n}}}
a){{{180(n-2)=165n}}}
{{{180n-360=165n}}}
{{{15n=360}}}
{{{n=24}}}
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b) {{{180(n-2)=171n}}}
{{{180n-360=171n}}}
{{{9n=360}}}
{{{n=40}}}
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c) {{{180(n-2)=75n}}}
{{{180n-360=75n}}}
{{{105n=360}}}
{{{n=24/7}}} <--- Not an integer
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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d) {{{180n-360=40n}}}
{{{180n-360=40n}}}
{{{140n=360}}}
{{{n=18/7}}} <--- Not an integer
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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Only a and b are valid interior angles.