Question

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

Answer 1

In ||gm ABCD,

$\angle D={135}^{\circ }$

But, $\angle A+\angle D={180}^{\circ }$

$\left(Sumofconsecutiveangles\right)$

$\Rightarrow \angle A+{135}^{\circ }={180}^{\circ }$

$\Rightarrow \angle A={180}^{\circ }-{135}^{\circ }={45}^{\circ }$

$\because \angle B=\angle D$ (Opposite angles of a || gm)

$\therefore \angle B={135}^{\circ }$