Question

Find the value of x.

Short answer

The value of$x$ is $\mathbf{41}\mathbf{°}$.

Step-by-step solution

Step 1. Name the given figure and highlight ∠x.

Step 2. Description of step.

Consider $\mathrm{\Delta }ABD$and $\mathrm{\Delta }BCD$, from the given figure it can be observed that, $\overline{AD}\cong \overline{CD},\overline{AB}\cong \overline{CB}$and $\overline{BD}$is common side to both the triangles. Therefore, by SAS postulate,

$m\angle A=m\angle C=98$

Step 3. Description of step.

Consider$\mathrm{\Delta }BCD$ in which$\overline{CD}\cong \overline{CB}$ it implies that$\mathrm{\Delta }BCD$ is an isosceles triangle.

Therefore,

$$\begin{gathered} \angle CBD\cong \angle BDC \\ \angle CBD=x \end{gathered}$$

Step 4. Apply an angle sum theorem.

Consider$\mathrm{\Delta }BCD$ such that,

$$\begin{gathered} m\angle CBD+m\angle BCD+m\angle BDC=180 \\ x+98+x=180 \\ 2x+98=180 \\ 2x=82 \\ x=41 \end{gathered}$$

Therefore, the value of $x$is $41°$.