AB is parallel to CD. A transversal PQ intersects AB and CD at E and F, respectively, and ∠PEB = 38°. G is a point between AB and CD such that ∠BEG = 24° and ∠GFE = 29°. What is the measure of ∠EGF?
33°
P–E–F–Q is a straight line (the transversal), with P on the side of AB away from CD. Since ∠PEB = 38°, the angle on the other side of EB along the line is ∠BEF = 180° − 38° = 142°.
G lies between AB and CD, so ray EG lies inside ∠BEF. Hence ∠GEF = ∠BEF − ∠BEG = 142° − 24° = 118°.
In triangle EGF, ∠GEF = 118° and ∠GFE = 29°.
By the angle sum property, ∠EGF = 180° − 118° − 29° = 33°.
Hence, the answer is 33°.
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