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{{ printedBook.courseTrack.name }} {{ printedBook.name }} To find the value of $x$ 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. $AX≅XBCY≅YB $ This means that $X$ and $Y$ are the midpoints of $AB$ and $CB,$ respectively. Therefore, $XY$ is a midsegment of $△ABC.$ The Triangle Midsegment Theorem tells us that, if a segment joins the midpoints of two sides of a triangle, then the segment is $half$ as long as the third side. $XY=21 AC $ Finally, we will substitute the given values into this equation to find $m.$ $m=21 (31)⇔m=15.5 $