The ratio of the 3 angles of a quadrilateral | vedclass

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(D) Let the three angles of the quadrilateral be $13x^{\circ}$,$9x^{\circ}$,and $5x^{\circ}$ respectively.The sum of all interior angles of a quadrila

Vedclass · Accepted Answer

$96$

Vedclass · Answer

(D) Let the three angles of the quadrilateral be $13x^{\circ}$,$9x^{\circ}$,and $5x^{\circ}$ respectively.The sum of all interior angles of a quadrilateral is $360^{\circ}$.Given the $4^{th}$ angle is $36^{\circ}$,we have:$13x + 9x + 5x + 36^{\circ} = 360^{\circ}$$27x = 360^{\circ} - 36^{\circ}$$27x = 324^{\circ}$$x = \frac{324}{27} = 12$The angles are:$1^{st} = 13 	imes 12 = 156^{\circ}$$2^{nd} = 9 	imes 12 = 108^{\circ}$$3^{rd} = 5 	imes 12 = 60^{\circ}$$4^{th} = 36^{\circ}$The largest angle is $156^{\circ}$ and the second smallest angle is $60^{\circ}$ (since $36 Difference $= 156^{\circ} - 60^{\circ} = 96^{\circ}$.

The ratio of the $3$ angles of a quadrilateral is $13: 9: 5$. The value of the $4^{th}$ angle of the quadrilateral is $36^{\circ}$. What is the difference between the largest and the second smallest angles of the quadrilateral? (in $^{\circ}$)

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