We have the following:
The sum of all the angles within a circle is equal to 360 degrees, therefore
[tex]\begin{gathered} 360=UV+VW+XW+XY+YU \\ UV=XW=108 \\ XY=VW=55 \end{gathered}[/tex]
replacing:
[tex]\begin{gathered} 360=108+55+108+55+YU \\ YU=360-108-55-108-55 \\ YU=34 \end{gathered}[/tex]
Therefore the mean angle YU is equal to 34 °
