AB is parallel to CD. A transversal PQ intersects AB and CD at E and F, respectively, and ∠PEB = 56°. G is a point between AB and CD such that ∠BEG = 32° and ∠GFE = 47°. What is the measure of ∠EGF?​

Correct option is D

Given:

AB is parallel to CD.

Transversal PQ intersects AB and CD at E and F respectively.

∠PEB = 56º
∠BEG = 32º
∠GFE = 47º

Formula used:
In a triangle, the sum of angles is 180º.

∠GEF + ∠GFE + ∠EGF = 180º

Solution:

∠BEG = 32°

∠GFE = 47°

∠GEF = 180° − (∠BEG + ∠PEB)
∠GEF = 180° − (32° + 56°)
∠GEF = 180° − 88°
∠GEF = 92°

Now, ∠GEF + ∠GFE + ∠EGF = 180°
92° + 47° + ∠EGF = 180°
139° + ∠EGF = 180°
∠EGF = 180° − 139°
∠EGF = 41°

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