Question

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

• A. $\angle A=\angle C={45}^{\circ },\angle B=\angle D={135}^{\circ }$
• B. $\angle A=\angle C={35}^{\circ },\angle B=\angle D={135}^{\circ }$
• C. $\angle A=\angle C={55}^{\circ },\angle B=\angle D={135}^{\circ }$
• D. None of the above

Answer 1

Answer: (A)

$\angle A=\angle C={45}^{\circ },\angle B=\angle D={135}^{\circ }$

Given: In $ABCD,$ $\angle B={135}^{\circ }$

We know that adjacent angles of a parallelogram are supplementary

So, $\angle A+\angle B={180}^{\circ }$
$\Rightarrow \angle A=180-135$
$\Rightarrow \angle A={45}^{\circ }$

And the opposite angles of a parallelogram are equal.

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

And $\angle A=\angle C={45}^{\circ }$