#### Answer

$\overline{BC}$

#### Work Step by Step

Let's take a look first at the angles in this triangle. We have an exterior angle, which will be supplementary to the interior angle $\angle A$; therefore, $\angle A$ of the triangle can be calculated by the following equation:
$m \angle A = 180 - 85$
Subtract to find the measure of $\angle A$:
$m \angle A = 95$
We know that $\angle A$ is the largest angle because the sum of the measures of the other two angles has to be $180^{\circ} - 95^{\circ}$ or $85^{\circ}$.
$\overline{BC}$ would be the longest because it is opposite the largest angle in a triangle where two of the angles are not congruent.