Answer:
x=18
Step-by-step explanation:
Let look at the triangle. Look at side JUI. Notices how it says JU is congruent to UI. By this definition, U must be the midpoint of J and I. The same applies for line JTK. T is the midpoint of J and K. Since J is the vertex of the triangle between K and I. Triangle JUT is the midsegment of triangle KJI. Using the triangle midsegment theorem, UT is parallel to KI Also. The theorem also states that UT is half the length of KI Also.
This is the theorem,
The Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long
So the equation is
[tex]2(3x - 43) = 4 + x[/tex]
[tex]6x - 86 = 4 + x[/tex]
[tex]5x - 86 = 4[/tex]
[tex]5x = 90[/tex]
[tex]x = 18[/tex]
