We know that AB || CD and EF is a transversal
From the figure we know that ∠EGB and ∠GHD are corresponding angles
So we get
∠EGB = ∠GHD = 35o
From the figure we know that ∠GHD and ∠QHP are vertically opposite angles
So we get
∠GHD = ∠QHP = 35o
We know that the sum of all the angles in triangle DQHP is 180o.
∠PQH + ∠QHP + ∠QPH = 180o
By substituting the values we get
∠PQH + 35o + 90o = 180o
On further calculation
∠PQH = 180o – 35o – 90o
By subtraction
∠PQH = 180o – 125o
∠PQH = 55o
Therefore, ∠PQH = 55o