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.

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.

Philoid · Accepted Answer

EGB = QHP (Alternate Exterior Angles) = 35^O

QPH = 90^O

So, in triangle QHP we have,

QPH + QHP + PQH = 180^O

90^O + 35^O + PQH = 180^O

PQH = 180^O – 90^O – 35^O

= 55^O