Question

ABCD is a parallelogram in which $\angle A={70}^{\circ }$, compute $\angle B,\angle C$ and $\angle D$.

Answer 1

In parallelogram ABCD,

$\angle A={70}^{\circ }$
But $\angle A+\angle B={180}^{\circ }$
(Sum of adjacent angles)
$\Rightarrow {70}^{\circ }+\angle B={180}^{\circ }\Rightarrow \angle B={180}^{\circ }-{70}^{\circ }={110}^{\circ }$
But $\angle C=\angle A$ and $\angle D=\angle B$
(Opposite angles)
$\therefore \angle C={70}^{\circ }$ and $\angle D={110}^{\circ }$
Hence $\angle B={110}^{\circ },\angle C={70}^{\circ }$ and $\angle D={110}^{\circ }$