Question

Use the information given in the following figure to find the value of $x$.

• A. ${40}^o$
• B. ${50}^o$
• C. ${45}^o$
• D. ${35}^o$

Answer 1

The correct option is A ${40}^o$

Let the quadrilateral be $ABCD$ and let $CD$ extend to $E$.

Let $\angle A={80}^o,\angle B={56}^o,\angle C=3x-6^o$

Then, $\angle EDC$ is a linear angle.

$\therefore \angle ADC$ $={180}^o-{70}^o={110}^o$

We know, by angle sum property,

the sum of interior angles of a quadrilateral$={360}^o$

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

$\Rightarrow {80}^o+{56}^o+3x-6^o+{110}^o={360}^o$

$\Rightarrow 3x+{240}^o={360}^o$

$\Rightarrow 3x={360}^o-{240}^o={120}^o$

$\Rightarrow x={40}^o$.

Therefore, option $A$ is correct.