Question

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

• A. $36{}^{\circ }$, $56{}^{\circ }$ $112{}^{\circ }$ $156{}^{\circ }$
• B. $36{}^{\circ }$, $60{}^{\circ }$ $112{}^{\circ }$ $156{}^{\circ }$
• C. $36{}^{\circ }$, $56{}^{\circ }$ $108{}^{\circ }$ $156{}^{\circ }$
• D. $36{}^{\circ }$, $60{}^{\circ }$ $108{}^{\circ }$ $156{}^{\circ }$

Answer 1

The correct option is D $36{}^{\circ }$, $60{}^{\circ }$ $108{}^{\circ }$ $156{}^{\circ }$

We know that,

Sum of the interior angles of a quadrilateral $=360{}^{\circ }$

According to the question,

$3x+5x+9x+13x=360{}^{\circ }$

$30x=360{}^{\circ }$

$x=12{}^{\circ }$

Therefore, angles in the quadrilateral will be,

$\Rightarrow 3x=3\times 12{}^{\circ }=36{}^{\circ }$

$\Rightarrow 5x=5\times 12{}^{\circ }=60{}^{\circ }$

$\Rightarrow 9x=9\times 12{}^{\circ }=108{}^{\circ }$

$\Rightarrow 13x=13\times 12{}^{\circ }=156{}^{\circ }$

Hence, this is the required result.