Question
Download Solution PDFAB 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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
Calculation:
∠BEG = 32º
∠GFE = 47º
⇒ ∠GEF = 180º - (∠BEG + ∠PEB)
⇒ ∠GEF = 180º - (32º + 56º)
⇒ ∠GEF = 180º - 88º
⇒ ∠GEF = 92º
Now, ∠GEF + ∠GFE + ∠EGF = 180º
⇒ 92° + 47° + ∠EGF = 180º
⇒ 139° + ∠EGF = 180º
⇒ ∠EGF = 180° - 139°
⇒ ∠EGF = 41°
∴ The corect answer is option (3).
Last updated on Jul 19, 2025
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