Question

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

Answer 1

1) Opposite angles in a parallelogram are equal.

2) Adjacent angles in a parallelogram are supplementary $\left(sumis{180}^0\right)$

$\therefore \angle B=\angle D={135}^0$ (opposite angles)

$\angle A+\angle B={180}^0$ (adjacent angles)

$\angle A=180-135$

$\angle A={45}^0$