# 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).