Geometry math question

we know that KUCN=105
CN=51
HMKU=96
HM=HMKU-MKU=96-78=18
we know that JN=JK+KN=82+105=187
JN=JH+HM+MKU+UC+CN
187=22+18+78+UC+51
UC=18.
the difference between 96 and 78 is 18 which is the length of HM which is equal to UC therefore making UC 18 as well.