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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,
=> 3x = 3 × $$12^\circ$$ = $$36^\circ$$
=>5x = 5 × $$12^\circ$$ = $$60^\circ$$
=> 9x = 9 × $$12^\circ$$ = $$108^\circ$$
=> 13x = 13 × $$12^\circ$$ = $$156^\circ$$