Question

Determine the value of x in given figure?

Answer 1

R.E.F image

$\angle ACB={180}^{\circ }-2x^{\circ }$___(1)

$\angle ABC={180}^{\circ }-(2x-{15}^{\circ })$

$={180}^{\circ }-2x+{15}^{\circ }$

$\angle ABC={195}^{\circ }-2x^{\circ }$___(2)

In $△ABC,$

$\angle CAB+\angle ABC+\angle ACB={180}^{\circ }$ [sum of all $\angle s$ of a $△$ is ${180}^{\circ }]$

$x^{\circ }+({195}^{\circ }-2x^{\circ })+({180}^{\circ }-2x^{\circ })={180}^{\circ }$

$\Rightarrow x^{\circ }+{375}^{\circ }-4x^{\circ }={180}^{\circ }$

$\Rightarrow {375}^{\circ }-{180}^{\circ }=3x^{\circ }$

$\Rightarrow {195}^{\circ }=3x^{\circ }$

$\Rightarrow x^{\circ }=\frac{195}{3}$

$\Rightarrow x^{\circ }={65}^{\circ }$