What is the missing statement and the missing reason in step 5?

\begin{tabular}{l|l|l}
\multicolumn{2}{c|}{\textbf{Statements}} & \multicolumn{1}{c}{\textbf{Reasons}} \\
\hline
1. [tex]$m \angle ADE = 60^{\circ}$[/tex] & 1. & Given \\
[tex]$m \angle CDF = (3x + 15)^{\circ}$[/tex] & & \\
2. [tex]$\angle ADE$[/tex] and [tex]$\angle CDF$[/tex] are vertical angles & 2. & Definition of vertical angles \\
3. [tex]$\angle ADE \approx \angle CDF$[/tex] & 3. & Vertical angles are congruent \\
4. [tex]$m \angle ADE = m \angle CDF$[/tex] & 4. & Definition of congruent angles \\
5. [tex]$60 = 3x + 15$[/tex] & 5. & Substitution \\
6. [tex]$45 = 3x$[/tex] & 6. & Subtraction property of equality \\
7. [tex]$x = 15$[/tex] & 7. & Division property of equality \\
\end{tabular}

Question

27-07-2024
Mathematics

Answered

What is the missing statement and the missing reason in step 5?

\begin{tabular}{l|l|l}
\multicolumn{2}{c|}{\textbf{Statements}} & \multicolumn{1}{c}{\textbf{Reasons}} \\
\hline
1. [tex]$m \angle ADE = 60^{\circ}$[/tex] & 1. & Given \\
[tex]$m \angle CDF = (3x + 15)^{\circ}$[/tex] & & \\
2. [tex]$\angle ADE$[/tex] and [tex]$\angle CDF$[/tex] are vertical angles & 2. & Definition of vertical angles \\
3. [tex]$\angle ADE \approx \angle CDF$[/tex] & 3. & Vertical angles are congruent \\
4. [tex]$m \angle ADE = m \angle CDF$[/tex] & 4. & Definition of congruent angles \\
5. [tex]$60 = 3x + 15$[/tex] & 5. & Substitution \\
6. [tex]$45 = 3x$[/tex] & 6. & Subtraction property of equality \\
7. [tex]$x = 15$[/tex] & 7. & Division property of equality \\
\end{tabular}

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-07-27T15:13:22-04:00

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