Question
In the following figure,
If $\angle BAD = 96^\circ,$ find $\angle BCD$ and $\angle BFE.$
If $\angle BAD = 96^\circ,$ find $\angle BCD$ and $\angle BFE.$
✓
Answer
$ABCD$ is a cyclic quadrilateral
$ \therefore \angle BAD +\angle BCD =180^{\circ} $
(pair of opposite angles in a cyclic quadrilateral are supplementary)
$ \Rightarrow \angle BCD =180^{\circ}-96^{\circ}=84^{\circ}$
$\therefore \angle BCE =180^{\circ}-84^{\circ}=96^{\circ} $
Similarly, $BCEF$ is a cyclic quadrilateral
$ \therefore \angle B C E+\angle B F E=180^{\circ} $
(pair of opposite angles in a cyclic quadrilateral are supplementary)
$ \therefore \angle B F E=180^{\circ}-96^{\circ}=84^{\circ} $
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