InterviewSolution
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InterviewSolution
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The number of diagonals of a regular polygon is 27. Then, find the measure of each of the interior angles of the polygon. |
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Answer» Let number of sides of a polygon be n. `implies" ""Number of diagonals"=(n(n-3))/(2)` `therefore" "(n(n-3))/(2)=27` `" "n(n-3)=54` `{:(implies,n^(2)-3n-54=0,),(implies,(n-9)(n+6)=0,),(therefore,n-9=0orn+6=0,),(implies,n=9orn= -6,("no.of sides connot be negative")),(therefore,n=9,):}` `therefore` It is a 9-sided polygon. `therefore` Each interior angle `=((n-2))/(n)xx180^(@)=((9-2))/(9)xx180^(@)=140^(@)` |
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