Question
In a parallelogram $ABCD, \angle\text{D}=135^\circ$, determine the measure of $\angle\text{A}$ and $\angle\text{B}$.
✓
Answer
In parallelogram $ABCD,$
$\angle\text{D}=135^\circ$
But $\angle\text{A}+\angle\text{D}=180^\circ$ (Sum of adjacent angles)
$\angle\text{A}+135^\circ=180^\circ$
$\angle\text{A}=180^\circ-135^\circ$
$\angle\text{A}=45^\circ$
But $\angle\text{B}=\angle\text{D}$ (Opposite angles)
$\angle\text{B}=135^\circ$
Hence,
$\angle\text{A}=45^\circ$
and
$\angle\text{B}=135^\circ$
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