  We continue to investigate the relation between the Mahler measure of certain
two variable polynomials, the values of the Bloch--Wigner dilogarithm $D(z)$
and the values $\zeta_F(2)$ of zeta functions of number fields. Specifically,
we define a class $\A$ of polynomials $A$ with the property that $\pi m(A)$ is
a linear combination of values $D$ at algebraic arguments. For many polynomials
in this class the corresponding argument of $D$ is in the Bloch group, which
leads to formulas expressing $\pi m(A)$ as a linear combination with
unspecified rational coefficients of $V_F$ for certain number fields $F$ ($V_F
:= c_F\zeta_F(2)$ with $c_F>0$ an explicit simple constant). The class $\A$
contains the $A$-polynomials of cusped hyperbolic manifolds. The connection
with hyperbolic geometry often provides means to prove identities of the form
$\pi m(A)= r V_F$ with an explicit value of $r\in \Q^*$. We give one such
example in detail in the body of the paper and in the appendix.
