Find the value of .
Step 1: Establish that and are similar.
Since and are parallel lines crossed by transversal , and
are corresponding angles and equal in measure.
and also share a common angle at .
If two angles of one triangle are equal in measure to two angles of another triangle, then the triangles are similar. Therefore, and must be similar.
Step 2: Find the value of .
Since the triangles are similar, their corresponding side lengths are proportional to each other. Therefore,