Finding angle of triangle

Question

In a triangle ABC, M is the midpoint of BC, P is any point on AM and PE, PF are perpendiculars to AB, AC respectively. If EF is parallel to BC, then find value of angle A

I tried extending BA to Point D such that DC becomes parallel to AM but I couldn't figure it out......Plz help Thank you

Answer 1

There's not enough information to find angle $A$.

Let $\Delta ABC$ be an arbitrary isosceles triangle with base angles at $B$ and $C$.

Then the hypothesis is satisfied but angle $A$ can take any value strictly between $0^\circ$ and $180^\circ$.