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(A) Let the angles of the quadrilateral be $3x, 5x, 9x$,and $13x$.Since the sum of all the interior angles of a quadrilateral is $360^{\circ}$,we have

Vedclass · Accepted Answer

$36^{\circ}, 60^{\circ}, 108^{\circ}, 156^{\circ}$

Vedclass · Answer

(A) Let the angles of the quadrilateral be $3x, 5x, 9x$,and $13x$.Since the sum of all the interior angles of a quadrilateral is $360^{\circ}$,we have:$3x + 5x + 9x + 13x = 360^{\circ}$Combining the terms:$30x = 360^{\circ}$Solving for $x$:$x = \frac{360^{\circ}}{30} = 12^{\circ}$Now,calculate each angle:$3x = 3 	imes 12^{\circ} = 36^{\circ}$$5x = 5 	imes 12^{\circ} = 60^{\circ}$$9x = 9 	imes 12^{\circ} = 108^{\circ}$$13x = 13 	imes 12^{\circ} = 156^{\circ}$Thus,the angles of the quadrilateral are $36^{\circ}, 60^{\circ}, 108^{\circ}$,and $156^{\circ}$.

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

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