Question
In a parallelogram ABCD, if $\angle\text{B}=135^\circ,$ determine the measure of its other angles.
✓
Answer
We have, $\angle \text{B}=135^\circ$ Since ABCD is a parallelogram$\therefore\angle\text{A}=\angle\text{C},\angle\text{B}=\angle\text{D}$ and $\angle\text{A}+\angle\text{B}=180^\circ$
$\Rightarrow\angle\text{A}+135^\circ=180^\circ$
$\Rightarrow\angle\text{A}=45^\circ$
$\Rightarrow\angle\text{A}=\angle\text{C}=45^\circ$ and $\angle\text{B}=\angle\text{D}=135^\circ$
$\Rightarrow\angle\text{A}+135^\circ=180^\circ$
$\Rightarrow\angle\text{A}=45^\circ$
$\Rightarrow\angle\text{A}=\angle\text{C}=45^\circ$ and $\angle\text{B}=\angle\text{D}=135^\circ$
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