Corrected Latitude

The initial latitude for S $44-18-38$ W$204\mathrm{.}75$ is:

$-146\mathrm{.}5117$

The residual for the latitudes is $-0\mathrm{.}0148$

The sum of the distances around the traverse is $769\mathrm{.}35\text{'}$

What is the corrected latitude?

Question $16$ options:

$-146\mathrm{.}5156$

$-146\mathrm{.}5265$

$-146\mathrm{.}5078$

$-146\mathrm{.}4969$