Question

In the given figure, AB || CD and EF is a transversal, cutting them at G and H, respectively. If ∠EGB = 35° and QP ⊥ EF, find the measure of ∠PQH.

Answer 1

We have:
$\angle EGB=\angle GHD=35°\left[\text{Corresponding Angles}\right]$
Also,
$\angle GHD=\angle PHQ=35°\left[\text{Vertically-Opposite Angles}\right]$
Now, in $∆PQH$, we have:
$$\begin{gathered} \angle HPQ+\angle PQH+\angle PHQ=180°\left[\text{Sum of the angles of a triangle}\right] \\ \Rightarrow 90°+\angle PQH+35°=180° \\ \Rightarrow \angle PQH=55° \end{gathered}$$