Question

In the given figure, AB || CD and EF || GH. Find the values of x, y, z and t.

Answer 1

In the given figure,
$$\begin{gathered} x=60°\left[\text{Vertically-Opposite Angles}\right] \\ \angle PRQ=\angle SQR\left[\text{Alternate Angles}\right] \\ y=60° \\ \angle APR=\angle PQS\left[\text{Corresponding Angles}\right] \\ \Rightarrow 110°=\angle PQR+60°\left[\because \angle PQS=\angle PQR+\angle RQS\right] \\ \Rightarrow \angle PQR=50° \end{gathered}$$
$$\begin{gathered} \angle PQR+\angle RQS+\angle BQS=180°\left[\text{Since AB is a straight line}\right] \\ \Rightarrow 50°+60°+z=180° \\ \Rightarrow 110°+z=180° \\ \Rightarrow z=70° \end{gathered}$$
$$\begin{gathered} \angle DSH=z\left[\text{Corresponding Angles}\right] \\ \Rightarrow \angle DSH=70° \\ \therefore \angle DSH=t\left[\text{Vertically-Opposite Angles}\right] \\ \Rightarrow t=70° \\ \therefore x=60°,y=60°,z=70°\text{and}t=70°. \end{gathered}$$