Question

Find the value of $x$ in given figure.

Answer 1

Produce $CD$ to cut $AB$ at $E.$

Now, in $\Delta BDE,$ we have$,$

Exterior $\angle CDB=\angle CEB+\angle DBE$

$\Rightarrow x=\angle CEB+45$ …..$\left(i\right)$

In $\Delta AEC,$ we have$,$

Exterior $\angle CEB=\angle CAB+\angle ACE$

$=55+30=85$

Putting $\angle CEB=85$ in $\left(i\right),$ we get$,$

$x=85+45=130$

$\therefore x=130$