Certainly! Let's piece together the missing statement and reason in step 5 based on the given context:
[tex]\[
\begin{tabular}{l|l|l}
\multicolumn{2}{c|}{Statements} & \multicolumn{1}{c}{Reasons} \\
\hline
1. & $m \angle A D E = 60^\circ$ & given \\
2. & $m \angle C D F = (3x + 15)^\circ$ & given \\
3. & $\angle A D E$ and $\angle C D F$ are vertical angles & definition of vertical angles \\
4. & $\angle A D E \cong \angle C D F$ & vertical angles are congruent \\
5. & $m \angle A D E = m \angle C D F$ & definition of congruent angles \\
6. & $60 = 3x + 15$ & substitution \\
7. & $45 = 3x$ & subtraction property of equality \\
8. & $x = 15$ & division property of equality \\
\end{tabular}
\][/tex]
In step 5, based on the information provided, the missing statement is [tex]$60 = 3x + 15$[/tex]. This comes from setting the measure of [tex]$\angle ADE$[/tex] equal to the measure of [tex]$\angle CDF$[/tex] as given by the substituted expressions.
The reason for this statement is "substitution" because we are substituting the given measures into the equality due to their congruence.
So, the detailed step-by-step solution missing in step 5 is:
Statement: [tex]\(60 = 3x + 15\)[/tex]
Reason: substitution
