# Construction Is A Piece Of Cake! Right? (Part-4)

Geometry Level 5

Sanskar, influenced by Mohit, Akshat and Anshuman, took two parallel lines $$PQ$$ and $$MN$$ (as shown in the figure) such that $$MN<PQ$$, and started doing aimless constructions, the steps of which are given below:

($$1$$) He marked four points $$A, B, C \mathrm{ and } D$$ such that $$AB=BC=CD$$ and then he drew a perpendicular on $$C$$ and marked a point $$F$$ on it such that $$AB=CF$$.

($$2$$) Then he joined $$AF$$ and marked a point $$E$$ on $$PQ$$ such that $$DE=AF$$ and $$E$$ doesn't lies on $$PD$$.

($$3$$) He then joined $$EN$$ which meets $$AM$$ at $$X$$ (both lines extended).

($$4$$) Then he joined $$CX$$ which intersects $$MN$$ at $$G$$ and then constructed $$\bigtriangleup MHN$$ such that $$MH=GN$$ and $$HN=MN$$

Sanskar then wondered what $$\angle MNH$$ could possibly be equal to (in degrees).

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