Question

Quadrilateral $ABCD$ is a parallelogram. Find the value of $x$ and measure of all the angles.

Answer 1

$2x-7^o=4x-{21}^o$ (Since opposite angles of a parallelogram are equal)

$\Rightarrow 4x-2x={21}^o-7^o$

$\Rightarrow 2x=14$

$\Rightarrow x=7^o$

$\angle D=2x-7^o=2\times 7^o-7^o=7^{\circ }$

$\angle B=4x-{21}^o=4\times 7^o-{21}^o=7^{\circ }$

Now, $\angle A+\angle D={180}^{\circ }$

$\Rightarrow \angle A+7^{\circ }={180}^{\circ }$

$\Rightarrow \angle A={180}^{\circ }-7^{\circ }$

$\Rightarrow \angle A={173}^{\circ }$

$\angle C=\angle A={173}^{\circ }$ (Since opposite angles of a parallelogram are equal)

Therefore $\angle A=\angle C={173}^{\circ }$

and $\angle B=\angle D=7^{\circ }$