AB is parallel to CD. A transversal PQ intersects AB and CD at E and F, respectively, and ∠PEB = 75°. G is a point between AB and CD such that ∠BEG = 45° and ∠GFE = 19°. What is the measure of ∠EGF?
101°
P, E, F and Q lie on the transversal in that order, so ∠PEB and ∠BEF form a linear pair.
∠BEF = 180° − 75° = 105°.
G lies between the lines inside ∠BEF, so ∠GEF = ∠BEF − ∠BEG = 105° − 45° = 60°.
In △EGF: ∠EGF = 180° − ∠GEF − ∠GFE = 180° − 60° − 19° = 101°.
Hence, the answer is 101°.
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