Question

Find the numerical value of $x^o$ from the diagram given below.

Answer 1

Given: $AC=AD$, $AD=BD$, $\angle BAM={75}^{\circ }$
In $△ADC$,
$AD=CD$
$\angle ADC=\angle ACD=x$ (Isosceles triangle property)
In $△ABD$,
$\angle DBA=\angle DAB=y$
Also, $\angle DBA+\angle DAB=\angle ADC$ (Exterior angle property)
$y+y=x$
$y=\frac{x}{2}$
Now, In $△ABC$,
$\angle BAM=\angle ABC+\angle ACB$ (Exterior angle property)
$75=x+\frac{x}{2}$
$75=\frac{3x}{2}$
$x={50}^{\circ }$