Question

In a parallelogram ABCD, if $\angle B={135}^{\circ }$ , determine the meaures of its other angles.

Answer 1

In a || gm ABCD, $\angle B={135}^{\circ }$

$\therefore \angle D=\angle B=135°$ (Opposite angles of a ||gm)

But $\angle A+\angle B=180°$ (Sum of consecutive angles)

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

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

But $\angle C=\angle B={45}^{\circ }$ (Opposite angles of a || gm)

$\therefore$ Angles are ${45}^{\circ },{135}^{\circ },{45}^{\circ },{135}^{\circ }.$