Question

In the given figure, $AB=AC$ find the value of $x$.

Answer 1

By using the property, that the angles opposite to the equal sides are equal.

$AB=AC$

$\Rightarrow \angle D=\angle C={55}^{\circ }$

Now,

$\angle ADB+\angle ADC={180}^{\circ }$ [Linear Pair Angles]

$\Rightarrow {75}^{\circ }+\angle ADC={180}^{\circ }$

$\Rightarrow \angle ADC={105}^{\circ }$

By using the angle sum property in $△ADC,$

$\angle DAC+\angle ADC+\angle C={180}^{\circ }$

$\Rightarrow x+{105}^{\circ }+{55}^{\circ }={180}^{\circ }$

$\Rightarrow x={180}^{\circ }-{160}^{\circ }$

$\Rightarrow x={20}^{\circ }$