Question

Suppose $ABCD$ is a parallelogram in which $\angle A={108}^{\circ }$. Calculate $\angle B,\angle C$ and $\angle D$.

• A. ${72}^{\circ },{108}^{\circ },{72}^{\circ }$
• B. ${22}^{\circ },{108}^{\circ },{72}^{\circ }$
• C. ${108}^{\circ },{72}^{\circ },{108}^{\circ }$
• D. None of these

Answer 1

The correct option is A ${72}^{\circ },{108}^{\circ },{72}^{\circ }$

$\Rightarrow$ $ABCD$ is a parallelogram.

$\Rightarrow$ $\angle A={108}^o$ [ Given ]

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

$\therefore$ $\angle C={108}^o$

$\Rightarrow$ $\angle A+\angle D={180}^o$ [ Adjacent angles of parallelogram are supplementary ]

$\Rightarrow$ ${108}^o+\angle D={180}^o$

$\therefore$ $\angle D={72}^o$

$\Rightarrow$ $\angle D=\angle B$ [ Opposite angles of a parallelogram are equal ]

$\therefore$ $\angle B={72}^o$