Question

In the given figure AD divides $\angle BAC$ in the ration 1 : 3 and AD = DB betermine the value of X.

Answer 1

AD divides $\angle$ BAC in the ratio 1 : 3.

So, let $\angle BAD=y$ and $\angle DAC=3y$

Now,

$y+3y+108=180$

$4y=72$

$y=18$

Now, since AD = BD, therefore,

$\angle BAD=\angle ABD=y=18$

$\angle ADC=2y=36$

Therefore, in $△ADC$,

$x+36+54=180$

$x={90}^o$