Question
In a cyclic quadrilateral $ABCD$ if $AB || CD$ and $\angle\text{B}=70^\circ,$ find the remaining angles.
✓
Answer
We have, $\angle\text{B}=70^\circ$
Since, $ABCD$ is a cyclic quadrilateral
Then, $\angle\text{B}+\angle\text{D}=180^\circ$
$\Rightarrow70^\circ+\angle\text{D}=180^\circ$
$\Rightarrow\angle\text{D}=180^\circ-70^\circ=110^\circ$
Since, $AB || DC$
Then, $\angle\text{B}+\angle\text{C}=180^\circ$ [Co-interior angles]
$\Rightarrow70^\circ+\angle\text{C}=180^\circ$
$\Rightarrow\angle\text{C}=180^\circ-70^\circ=110^\circ$
Now, $\angle\text{A} +\angle\text{C}=180^\circ$ [Opposite angles of cyclic quad.]
$\Rightarrow\angle\text{A}+110^\circ=180^\circ$
$\Rightarrow\angle\text{A}=180^\circ-110^\circ=70^\circ$
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