Question

Find the value of $x$ in each case :

Answer 1

In $△ABC,$ by

Angle sum property

$\angle CAB+\angle ABC+\angle BCA={180}^{\circ }$

$\angle BCA={180}^{\circ }-{105}^{\circ }$

$\angle BCA={75}^{\circ }$

$\angle BCA=\angle DCE$ [Vertically Opp. Angles]

In $△CDE,$

$\angle CDE+\angle DEC+\angle ECD={180}^{\circ }$

${80}^{\circ }+{75}^{\circ }+\angle DEC={180}^{\circ }$

$\angle DEC={25}^{\circ }$

$x={25}^{\circ }$