Question

In the following figure find the value of $x$.

Answer 1

Step 1. Analyze the given figure.

From the above figure, $\angle ABC={53}^o$

$\overline{BC}$ $=\overline{AC}$ $\Rightarrow$ $\angle BAC=\angle ABC={53}^o$ (because angles opposite to equal sides are also equal).

$\angle ACB={180}^0-\angle ACD$ ( because $\angle ACB$ and $\angle ACD$ are linear pair angles).

Step 2. Find the value $x$ by applying the angle sum property of the triangle.

According to the angle sum property of the triangle in $△ABC$, $\angle ABC+\angle ACB+\angle BAC={180}^o$.

put the values of all given angles.

${53}^o+\angle ACB+{53}^o={180}^o$

$\angle ACB+{106}^o={180}^o$

$\angle ACB={180}^o-{106}^o$

$\angle ACB={74}^o$

$\angle ACD={180}^o-\angle ACB$ ( because $\angle ACB$ and $\angle ACD$ are linear pair angles).

$\angle ACD$ $={180}^o-{74}^o$

$\angle ACD$ $={106}^o$

Hence, the required value of $x$ is ${106}^o$.