Question

In the figure, sides AD and AB of cyclic quadrilateral ABCD are produced to E and F respectively. If $\angle CBF={130}^{\circ }and\angle CDE=x^{\circ },$ find the value of $x$.

Answer 1

ANSWER:
ABCD is a cyclic quadrilateral.
We know that in a cyclic quadrilateral, the exterior angle is equal to the interior opposite angle.
$\therefore \angle CBF=\angle CDA$
$\Rightarrow \angle CBF=({180}^{\circ }–x)$
$\Rightarrow {130}^{\circ }={180}^{\circ }–x[\because \angle CBF={130}^{\circ }]$
$\Rightarrow x=({180}^{\circ }–{130}^{\circ })={50}^{\circ }$
Hence, $x={50}^{\circ }$