  We extend the result of Lavrentiev which asserts that the harmonic measure
and the arc-length measure are $A_\infty$ equivalent in a chord-arc Jordan
domain. By using this result we extend the classical result of Lindel\"of to
the class of quasiconformal (q.c.) harmonic mappings by proving the following
assertion. Assume that $f$ is a quasiconformal harmonic mapping of the unit
disk $\mathbf{U}$ onto a Jordan domain. Then the function
$A(z)=\arg(\partial_\varphi(f(z))/z)$ where $z=re^{i\varphi}$, is well-defined
and smooth in $\mathbf{U}^*=\{z: 0<|z|<1\}$ and has a continuous extension to
the boundary of the unit disk if and only if the image domain has $C^1$
boundary.
