Question

In Fig., PQ || RS. Find the value of x.

Answer 1

$$\begin{gathered} \angle \mathrm{RCD}+\angle \mathrm{RCB}=180°\left(\mathrm{Linear}\mathrm{pair}\right) \\ \Rightarrow \angle \mathrm{RCB}=180°-130°=50° \\ \mathrm{In}△\mathrm{ABC}, \\ \angle \mathrm{BAC}+\angle \mathrm{ABC}+\angle \mathrm{BCA}=180°\left(\mathrm{Angle}\mathrm{sum}\mathrm{property}\right) \\ \Rightarrow \angle \mathrm{BAC}=180°-55°-50°=75° \end{gathered}$$