Step 1: Find the unknown angle measures in .
Since and are parallel to each other and crossed by transversal , and are alternate interior angles and equal in measure.
To find , subtract the sum of the other two angles measures from .
So, , , and .
Step 2: Arrange the side lengths in descending order.
For any triangle, the longest side is opposite to the greatest angle measure, and the shortest side is opposite to the smallest angle measure.
The greatest angle measure is , so is the longest side. The smallest angle measure is , so is the shortest side.
Therefore, the side lengths in descending order are: , , .