Geometry math question no Guessing and Please show work thank you

we are given that
[tex] HM=UC [/tex]
[tex] HM=UH-MU [/tex]
[tex] UH=96 [/tex]
[tex] MU=78 [/tex]
we can plug these values
and we get
[tex] HM=96-78 [/tex]
[tex] HM=18 [/tex]
Since,
[tex] HM=UC [/tex]
so,
[tex] UC=18 [/tex]............Answer