A polygon has 5 diagonals and one angle of that polygon is . If the re

SOLUTION

let number of sides be n, then

No. of diagonals =

⇒

⇒

⇒

⇒ n(n-5) + 2(n-5) = 0

⇒ (n+2)(n-5) = 0

⇒ n = 5, n = -2

But number of sides cannot equal to -2.

Hence the given polygon is a Pentagon.

One angle of the pentagon is .

Since, the remaining angles are in the ratio 1:2:3:4.

Let the remaining angles be x, 2x, 3x and 4x.

But the sum of interior angles of a pentagon =

According to question

⇒

⇒

⇒

Hence the angles of the pentagon are  and .

Hence the size of greatest angles =