Question

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

• A. $\angle$A = 45${}^o$
• B. $\angle$A = 145${}^o$
• C. $\angle$A = 35${}^o$
• D. $\angle$A = 75${}^o$

Answer 1

The correct option is A $\angle$A = 45${}^o$

$ABCD$ is a parallelogram, $\angle D=135$
We know, in a parallelogram, opposite angles are equal.
Thus, $\angle B=\angle D$
$=>\angle B=135$
Also, in a parallelogram opposites sides are parallel. Thus,
$AD\parallel BC$
Now, $AD\parallel BC$ and $AB$ is the transversal, then
$\angle A+\angle B=180$
$=>\angle A=180-135$
$=>\angle A=45$