The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.

Given: The ratios of the angles of quadrilateral are 3: 5: 9: 13.

Let the angles of the quadrilateral be 3x, 5x, 9x and 13x.

We know that, sum of angles of a quadrilateral = \(360^\circ\)
\(\Rightarrow \) 3x + 5x + 9x + 13x = \(360^\circ\)
\(\Rightarrow \) 30x = \(360^\circ\)
\(\therefore \) x = \(12^\circ\)

Thus, we get,
angles of quadrilateral
=> 3x = 3 × \(12^\circ\) = \(36^\circ\)
=>5x = 5 × \(12^\circ\) = \(60^\circ\)
=> 9x = 9 × \(12^\circ\) = \(108^\circ\)
=> 13x = 13 × \(12^\circ\) = \(156^\circ\)