We are given two chords of equal length, this means that the arc they form are equal, this means:
[tex]\text{mAC}=\text{mBD}[/tex]
Replacing the expressions for each arc we get:
[tex]5x+5=4x+27[/tex]
From this expression we can solve for "x" first by subtracting "4x" to both sides:
[tex]5x-4x+5=27[/tex]
Now we subtract 5 to both sides:
[tex]5x-4x=27-5[/tex]
Now we add like terms:
[tex]x=22[/tex]
Now we replace this value of "x" in the expression for arc BC-:
[tex]\text{mBC}=x+16[/tex]
Replacing the value of "x":
[tex]\begin{gathered} \text{mBC}=22+16 \\ \text{mBC}=38 \end{gathered}[/tex]
