Two parallel lines are intersected by a transversal. If one angle is 165 degrees, and another angle is labeled M, and a third angle is labeled 8K, find the values of M and K.

The image shows two parallel lines intersected by a transversal line. We will assume the horizontal lines are parallel.

The angle $165^\circ$ and angle $M$ are alternate exterior angles. When two parallel lines are intersected by a transversal, alternate exterior angles are equal.
Therefore:

First, find the interior angle on the bottom left, adjacent to $165^\circ$. Let's call this angle $\alpha$. Angles on a straight line sum to $180^\circ$.

Now, $\alpha$ and $8K$ are consecutive interior angles (also known as same-side interior angles). When two parallel lines are intersected by a transversal, consecutive interior angles are supplementary (sum to $180^\circ$).

The values are $M = 165^\circ$ and $K = \frac{165}{8}^\circ$.