Question

In a parallelogram ABCD, $m\angle A=(7x+40{)}^0$ and $m\angle C=(2x+60{)}^0$. Find the measures of $\angle B$ and $\angle D$ ?

Answer 1

Here, $ABCD$ is a parallelogram.

$\Rightarrow$ $\angle A=\angle C$ [ Opposite angles are equal in parallelogram ]

$\Rightarrow$ $7x+40=2x+60$

$\Rightarrow$ $5x=20$

$\Rightarrow$ $x=4$

$\Rightarrow$ $m\angle A=(7x+40{)}^o=(7\times 4+40{)}^o={68}^o$

$\Rightarrow$ $\angle A+\angle B={180}^o$ [ Sum of adjacent angles in parallelogram are supplementary ]

$\Rightarrow$ ${68}^o+\angle B={180}^o$

$\therefore$ $\angle B={112}^o$

$\Rightarrow$ $\angle B=\angle D={112}^o$ [ Opposite angles are equal in parallelogram ]

$\therefore$ Measure of $\angle B$ and $\angle D$ is ${112}^o$.