Answer
$m\angle CZD=34$
Work Step by Step
We know the measures of $\angle BZC$ and $\angle FZE$ are equal. We are given a value for $m\angle FZE$. Write an equation for $m\angle BZC$. Substitute to solve for x.
$m\angle BZC+m\angle CZD=m\angle BZD\longrightarrow$ angle addition postulate
$m\angle BZC=m\angle BZD-m\angle CZD\longrightarrow$ subtraction property of equality
$\angle BZC\cong\angle FZE\longrightarrow$ vertical angles theorem
$m\angle BZC=m\angle FZE\longrightarrow$ definition of congruency
$m\angle BZD-m\angle CZD=m\angle FZE\longrightarrow$ substitution
$107-x=2x+5\longrightarrow$ substitution
$107=3x+5\longrightarrow$ addition property of equality
$102=3x\longrightarrow$ subtraction property of equality
$34=x\longrightarrow$ division property of equality
$m\angle CZD=x=34$
