Question

In quadrilateral PQRS, if $\angle P={60}^{\circ }$ and $\angle Q:\angle R:\angle S=2:3:7,$ then find the measure of $\angle S.$

Answer 1

$\text{Let}\angle Q=2x,\angle R=3x\text{and}\angle S=7x$

$\text{Now,}\angle P+\angle Q+\angle R+\angle S={360}^{\circ }$

$\Rightarrow {60}^{\circ }+2x+3x+7x={360}^{\circ }$

$\Rightarrow 12x={300}^{\circ }$

$x=\frac{{300}^{\circ }}{12}={25}^{\circ }$

$\angle S=7x=7\times {25}^{\circ }={175}^{\circ }$