AMC 8 2020 Problem 16

Each of the points $A,B,C,D,E,$ and $F$ in the figure below represents a different digit from $1$ to $6.$ Each of the five lines shown passes through some of these points. The digits along each line are added to produce five sums, one for each line. The total of the five sums is $47.$ What is the digit represented by $B?$

$\textbf{(A) }1 \textbf{(B) }2 \textbf{(C) }3 \textbf{(D) }4 \textbf{(E) }5$