MHB Finding the Value of $n$ in a Rhombus $DBEF$

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In the discussion, the geometric properties of rhombus $DBEF$ formed within square $ABCD$ are analyzed. It is established that $CF$ is parallel to $BD$ and that $DF$ equals $DB$. The relationship between angles is highlighted, specifically that $\angle BDF$ is $n$ times $\angle F$, with $n$ being a natural number. The objective is to determine the value of $n$. The solution involves applying properties of angles in rhombuses and squares to derive the value of $n$.
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$ABCD $ is a square,$CF//BD$, and $DF=DB$,point $E,$ is on $CF$
given :$DBEF$ is a rhombus
if $\angle BDF=n\angle F$(here :$n\in N)$
please find :$n=?$
 
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Albert said:
$ABCD $ is a square,$CF//BD$, and $DF=DB$,point $E,$ is on $CF$
given :$DBEF$ is a rhombus
if $\angle BDF=n\angle F$(here :$n\in N)$
please find :$n=?$
 

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Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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