Answered

Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Join our platform to connect with experts ready to provide precise answers to your questions in various areas. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Given: \(m \angle ADE = 60^{\circ}\) and \(m \angle CDF = (3x + 15)^{\circ}\)

Prove: \(x = 15\)

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

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

Sagot :

GinnyAnswer
To solve the problem and to find the missing statement and reason in step 5, let's go through the detailed, step-by-step solution:

1. Given Information:
- \( m \angle ADE = 60^\circ \)
- \( m \angle CDF = (3x + 15)^\circ \)

Reason 1: Given.

2. Identify Vertical Angles:
- \( \angle ADE \) and \( \angle CDF \) are vertical angles.

Reason 2: Definition of vertical angles.

3. Vertical Angles are Equal:
- \( \angle ADE = \angle CDF \)

Reason 3: Vertical angles have equal measures.

4. Equal Measures:
- \( m \angle ADE = m \angle CDF \)

Reason 4: Definition of congruent angles.

5. Substitute the Given Values:
- Substitute the given values into the equation.
- \( 60 = 3x + 15 \)

Reason: Substitution.

6. Solve for \( x \):
- Subtract 15 from both sides:
[tex]\[ 60 - 15 = 3x \][/tex]
[tex]\[ 45 = 3x \][/tex]

Missing Statement and Reason:
- Statement: \( 45 = 3x \),
- Reason: Subtraction property of equality.

7. Solve for \( x \):
- Divide both sides by 3:
[tex]\[ \frac{45}{3} = x \][/tex]
[tex]\[ x = 15 \][/tex]

Reason: Division property of equality.

So, the missing statement and reason in step 5 are:

Statement: \( 45 = 3x \)

Reason: Subtraction property of equality.
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.