Question

Calculate the value of x in the given figure.

Answer 1

Join A and D to produce AD to E.
Then,
$$\begin{gathered} \angle CAD+\angle DAB=55°\text{and} \\ \angle CDE+\angle EDB=x° \end{gathered}$$
Side AD of triangle ACD is produced to E.
$\therefore \angle CDE=\angle CAD+\angle ACD...\left(i\right)$ (Exterior angle property)
Side AD of triangle ABD is produced to E.
$\therefore \angle EDB=\angle DAB+\angle ABD...\left(ii\right)$ (Exterior angle property)
$$\begin{gathered} \mathrm{Adding}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right)\mathrm{we}\mathrm{get}, \\ \angle CDE+\angle EDB=\angle CAD+\angle ACD+\angle DAB+\angle ABD \end{gathered}$$

$$\begin{gathered} \Rightarrow x°=\left(\angle CAD+\angle DAB\right)+30°+45° \\ \Rightarrow x°=55°+30°+45° \\ \Rightarrow x°=130° \\ \Rightarrow x=130 \end{gathered}$$