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 ≅ XB
CY ≅ YB
This means that X and Y are the midpoints of AB and CB, respectively. Therefore, XY is a midsegment of â–łABC. 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= 1/2 AC
Finally, we will substitute the given values into this equation to find x.
x=1/2( 30) ⇔ x=15
