Question

Find the values of the $x$ (in deg.) in the given figure

Answer 1

Given, $\angle ACP={57}^o$

Let $OA=OC=$ radius of circle

and Let $P$ be the external point from which $PC,PA$ tangents are drawn.

We know, $\angle OCP=\angle OAP={90}^o$

then $\angle OCA=\angle OAC=90-57={33}^o$

then, In $△AOC$ $\angle AOC=180-33-33={114}^o$

$\angle ABC=\frac{1}{2}\angle AOC=\frac{1}{2}\times 114={57}^o$

We know,

$AB=AC\angle ABC=\angle ACB={57}^o$

In $△ABCx=180-2\times 57={66}^o$