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Quantitative Aptitude
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NTPC Graduate Tier 1 2025 Shift-3 📅 05 Jun, 2025

AB is parallel to CD. A transversal PQ intersects AB and CD at E and F, respectively, and ∠PEB = 59°. G is a point between AB and CD such that ∠BEG = 50° and ∠GFE = 33°. What is the measure of ∠EGF?

A
76°
B
80°
C
74°
D
88°
Result Summary
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NTPC Graduate Tier 1
2025 • 05 Jun, 2025 • Shift-3
AB is parallel to CD. A transversal PQ intersects AB and CD at E and F, respectively, and ∠PEB = 59°. G is a point between AB and CD such that ∠BEG = 50° and ∠GFE = 33°. What is the measure of ∠EGF?
Correct Answer
76°
[Geometrical Mapping]: The transversal PQ cuts the parallel lines AB and CD. Since the exterior angle ∠PEB is 59°, the adjacent interior angle on the same st......
Ref/Book : NTPC Graduate Tier 1 2025
Ref. Subject Quantitative Aptitude
Chapter -
Ref. Topic Geometry
Pg. No -
💡 Analysis & Explanation
[Geometrical Mapping] ▼
The transversal PQ cuts the parallel lines AB and CD. Since the exterior angle ∠PEB is 59°, the adjacent interior angle on the same straight line, ∠BEF, is 180° - 59° = 121°.
[Internal Angle Breakdown] ▼
The problem states that point G creates an angle ∠BEG = 50°. Since G lies between the parallel lines, the remaining part of the interior angle at E is ∠GEF = ∠BEF - ∠BEG = 121° - 50° = 71°.
[Triangle Formation] ▼
Now, consider the triangle formed by points E, G, and F. We have determined that ∠GEF = 71°. The problem explicitly provides that ∠GFE = 33°.
[Final Angle Calculation] ▼
Using the fundamental property that the sum of angles in a triangle is 180°, we can find ∠EGF. Therefore, ∠EGF = 180° - (71° + 33°) = 180° - 104° = 76°.
Conclusion ▼
The exact measure of ∠EGF is 76°.
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