To find the value of in the given diagram, let's start by labeling the vertices of each of the smaller triangles.
Looking at the markings, we can note a couple key congruence relationships. This means that and are the midpoints of and respectively. Therefore, is a midsegment of The Triangle Midsegment Theorem tells us that, if a segment joins the midpoints of two sides of a triangle, then the segment is as long as the third side. Finally, we will substitute the given values into this equation to find