Question

In a parallelogram $ABCD$ find the measure of angle $B$ if one measures ${68}^{\circ }$.

Answer 1

Let $ABCD$ be the given parallelogram and $\angle A$ be the given angle.

$\therefore \angle A=68°$

As we know that, in a parallelogram opposite angles are equal.

$\therefore \angle C=\angle A=68°$

Let the measurement of $\angle B$ be $x°$.

$\therefore \angle D=\angle B=x°(\because \text{Opposite angles})$

Now as we know that sum of all the angles in a parallelogram is $360°$.

$\therefore 68°+x°+68°+x°=360°$

$\Rightarrow 2x°+136°=360°$

$\Rightarrow 2x°=360°-136°$

$\Rightarrow x°=\frac{224°}{2}=112°$

Hence the measure of all the $4$ angles of the parallelogram is $68°,112°,68°$ and $112°$.