Question
Download Solution PDFAB is parallel to CD. A transversal PQ intersects AB and CD at E and F, respectively, and ∠PEB = 59º. G is a point between AB and CD such that ∠BEG = 50º and ∠GFE = 33º. What is the measure of ∠EGF?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
AB is parallel to CD.
A transversal PQ intersects AB and CD at E and F, respectively.
∠PEB = 59º.
G is a point between AB and CD such that:
∠BEG = 50º
∠GFE = 33º
We need to find the measure of ∠EGF.
Formula Used:
Sum of angles in a triangle = 180º
Calculation:
Use linear pair on ∠PEB and ∠BEF
∠PEB + ∠BEF = 180° (on a straight line)
⇒ 59° + ∠BEF = 180°
So the angle ∠BEF = 180 - 59 = 121°
Now, ∠BEF = ∠BEG + ∠GEF
∠GEF = ∠BEF - ∠BEG
∠GEF = 121 - 50 = 71°
Use angle sum property in triangle EGF
∠GEF + ∠GFE + ∠EGF = 180°
⇒ 71° + 33° + ∠EGF = 180°
⇒ ∠EGF = 180° − 104° = 76°
∴ The measure of ∠EGF = 76°
Last updated on Jul 17, 2025
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