Question

In the given figure, if AB$=$BC and $\angle$ A $=\angle$C then find the value of x.

Answer 1

$In△BEC:$

$\angle EBC+\angle BEC+\angle BCE={180}^{\circ }$

$⟹{55}^{\circ }+x+\angle BCE={180}^{\circ }$

$⟹\angle BCE={125}^{\circ }-x-\left(1\right)In△BDA$

$⟹{55}^{\circ }+{75}^{\circ }+\angle BAD={180}^{\circ }$

$⟹\angle BAD={50}^{\circ }$

$\because \angle A=\angle C$

$⟹\angle BAD=\angle BCE$

$⟹\angle BCE={50}^{\circ }$

$puttingin\left(1\right)$

$⟹50=125-x$

$⟹x={75}^{\circ }$