The number of diagonals of a regular polygon is 27. Then, find the measure of each of the interior angles of the polygon.
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
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^(@)`