Answer
$M=Fe$
Work Step by Step
65.57% of one mole of the compound weighs $\frac{35.45g\ Cl}{1mol\ Cl}\times3=106.35g$. This means the whole compound weighs $106.35g\times\frac{100}{65.57}=162g$. Subtracting the weight of $Cl$ from the total weight gives us the molar mass of the unknown metal. $162-106.35=55.65$. Looking at the periodic table we see that the unknown metal is $Fe$.
