Yes! There is enough information to solve for x. x equals 23 degrees because we know that one angle measure is 23, and that this is a right triangle so another angle measure must be 90. Since we know 2 of the angle measures, we can find the third by subtracting from 180. Seeing as the mid-line bisects this angle and creates a shared side for the 2 triangles, we know the triangles must be congruent. We could also explain this using SAA if needed. To put it short, though, there are several ways we can prove that x=23.