AB 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?

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RRB NTPC Graduate Level CBT-I Official Paper (Held On: 05 Jun, 2025 Shift 3)
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  1. 80°
  2. 76° 
  3. 74°
  4. 88°

Answer (Detailed Solution Below)

Option 2 : 76° 
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Detailed Solution

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Given:

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:

qImage68692d51b3a3fadca5c9439c

 

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° 

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