Question

In a parallelogram ABCD, $\angle D={135}^{\circ }$ determine the measure of $\angle A$ and $\angle B$.

Answer 1

In parallelogram ABCD,

$\angle D={135}^{\circ }$
But $\angle A+\angle D={180}^{\circ }$
(Sum of adjacent angles)
$\Rightarrow \angle A+{135}^{\circ }={180}^{\circ }\Rightarrow \angle A={180}^{\circ }-{135}^{\circ }={45}^{\circ }$
But $\angle B=\angle D$

(Opposite angles)
$\therefore \angle B={135}^{\circ }$
Hence $\angle A={45}^{\circ }$ and $\angle B={135}^{\circ }$