Question

In a quadrilateral $PQRS$, if $\angle P=\angle R={100}^{\circ }$ and $\angle S={75}^{\circ }$, then $\angle Q=$ ......... .

• A. ${50}^{\circ }$
• B. ${85}^{\circ }$
• C. ${120}^{\circ }$
• D. ${360}^{\circ }$

Answer 1

Answer: (B)

${85}^{\circ }$

We know, by angle sum property, the sum of angles of a quadrilateral is ${360}^o$.

The given angles are $\angle P={100}^o,\angle R={100}^o,\angle S={75}^o,\angle Q$.

Then, $\angle P+\angle Q+\angle R+\angle S={360}^o$

$⟹$ ${100}^o+{100}^o+{75}^o+\angle Q={360}^o$.

$\Rightarrow$ $\angle Q={360}^o-({100}^o+{100}^o+{75}^o)$

$\Rightarrow$ $\angle Q={360}^o-{275}^o={85}^{\circ }$.

Therefore, the unknown angle is $\angle Q={85}^o$.

Hence, option $B$ is correct.