Question

In a quadrilateral $ABCD$, if $\angle$ $A=60$ ${}^o$ and $\angle$ $B:$ $\angle$ $C:$ $\angle$ $D=2:3:7$, then $\angle$ $D=$ ?

• A. $175$ ${}^o$
• B. $135$ ${}^o$
• C. $150$ ${}^o$
• D. None of these

Answer 1

The correct option is A $175$ ${}^o$

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

Given, $\angle B:\angle C:\angle D=2:3:7$.
Let the $\angle B=2x,\angle C=3x,\angle D=7x$ and $\angle A={60}^o$.
$\Rightarrow 2x+3x+7x+{60}^o={360}^o$
$\Rightarrow 12x={300}^o$
$\Rightarrow x={25}^o$.

$\therefore \angle D=7x=7\times {25}^o={175}^o$.

Hence, option $A$ is correct.