Question

If the quadrilateral $ABCD$ is a parallelogram. What is the value of $x$?

• A. ${45}^{\circ }$
• B. ${30}^{\circ }$
• C. ${36}^{\circ }$
• D. ${37}^{\circ }$

Answer 1

The correct option is C ${36}^{\circ }$

In parallelogram $ABCD,$

We know that the opposite angles of a parallelogram are equal.

Hence $\angle A=\angle C$

$\Rightarrow 3y=3x+3$ $...\left(1\right)$

and $\angle B=\angle D$

$\therefore \angle D=2y-5$ $...\left(2\right)$

We know that the sum of angles of a parallelogram is ${360}^{\circ }$

$\Rightarrow \left(3y\right)+(3x+3)+(2y-5)+(2y-5)=360$

$\Rightarrow 3y+3y+4y-10=360$

$\Rightarrow 10y-10=360$

$\Rightarrow 10y=360+10$

$\Rightarrow 10y=370$

$\Rightarrow y=\frac{370}{10}={37}^{\circ }$

Substitute $y={37}^{\circ }$ in $\left(1\right)$

$\Rightarrow 3\times \left({37}^{\circ }\right)=3x+3^{\circ }$

$\Rightarrow 111=3x+3$

$\Rightarrow 3x=111-3$

$\Rightarrow 3x=108$

$\Rightarrow x=\frac{108}{3}={36}^{\circ }$