AB is parallel to CD. A transversal PQ intersects AB and CD at E and F, respectively, and ∠PEB = 78°. G is a point between AB and CD such that ∠BEG = 18° and ∠GFE = 30°. What is the measure of ∠EGF?

Question

Question

This question was previously asked in

RRB Group D 2 Sept 2022 Shift 3 Official Paper

Answer 1

Given:

AB is parallel to CD. A transversal PQ intersects AB and CD at E and F, respectively, and ∠PEB = 78°.

G is a point between AB and CD such that ∠BEG = 18° and ∠GFE = 30°

Concept used:

Sum of angles on a straight line is 180^o.

Sum of all angles of a triangle is 180o.

Calculation:

angle2

=> ∠PEB + ∠BEG + ∠FEG = 180^o

=> 78^o + 18^o + ∠FEG = 180^o

=> ∠FEG = 84^o

Now , In triangle EGF,

∠GFE + ∠EGF + ∠FEG = 180

=> 30^o + ∠EGF + 84^o = 180^o

=> ∠EGF = 180^o - 84^o - 30^o

=> ∠EGF = 66^o

Hence, 'option 3' is the correct answer.