Question

In the adjoining figure, if $\angle A={90}^o$, then find $x$.

• A. $11$
• B. $19$
• C. $13$
• D. $20$

Answer 1

The correct option is B $19$

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

The given angles are $\angle A={90}^o,\angle B=6x-5^o,\angle C=7x-{15}^o,\angle D=2x+5^o$.

Then, $\angle A+\angle B+\angle C+\angle D={360}^o$

$⟹$ ${90}^o+6x-5^o+7x-{15}^o+2x+5^o={360}^o$

$⟹$ $15x+{75}^o={360}^o$

$⟹$ $15x={360}^o-{75}^o={285}^o$

$⟹$ $x={19}^o$.

Therefore, option $B$ is correct.