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.
Solution:
In the given figure, AB || CD and EF is a transversal.
∴ ∠PHQ = ∠EGB (Pair of alternate exterior angles)
⇒ ∠PHQ = 35°
In ∆PHQ,
∠PHQ + ∠QPH + ∠PQH = 180° (Angle sum property)
⇒ 35° + 90° + x = 180°
⇒ 125° + x = 180°
⇒ x = 180° − 125° = 55°
Thus, the measure of ∠PQH is 55°.