https://file.aiquickdraw.com/mathbot/file/1726236967338qoh9ooxs.jpg

To solve this geometry problem and determine the missing statement and reason in step 5, let's carefully analyze the information provided.

### Given:
- \( m\angle ADE = 60^\circ \)
- \( m\angle CDF = (3x + 15)^\circ \)
- Prove: \( x = 15 \)

The angles \( \angle ADE \) and \( \angle CDF \) are vertical angles, meaning they are congruent. Therefore, we can set their measures equal to each other:
\[
m\angle ADE = m\angle CDF
\]
This gives the equation:
\[
60 = 3x + 15
\]

Now, we'll follow the proof steps:

1. **Given**:
   - \( m\angle ADE = 60^\circ \)
   - \( m\angle CDF = (3x + 15)^\circ \)
2. **Definition of vertical angles**:
   - \( \angle ADE \) and \( \angle CDF \) are vertical angles.
3. **Congruence of vertical angles**:
   - \( m\angle ADE = m\angle CDF \)
   - So, \( 60 = 3x + 15 \).
4. **Subtraction property**:
   - \( 45 = 3x \), obtained by subtracting 15 from both sides.
5. **Division property**:
   - \( 15 = x \), obtained by dividing both sides by 3.

### Step 5:
In step 5, the equation becomes \( 15 = x \), and this is achieved by applying the division property of equality.

### The missing statement and reason are:
- **Statement**: \( 15 = x \)
- **Reason**: Division property of equality.

Thus, the correct answer is:
- **Statement: x = 15; Reason: division property of equality.**

---

Would you like further clarification or additional details on this proof?

Here are 5 related questions to expand on this:
1. How are vertical angles defined in geometry?
2. What other properties do vertical angles have besides being congruent?
3. What is the subtraction property of equality?
4. How can you use algebraic methods to solve for a variable in a geometric context?
5. What is the significance of congruent angles in proving geometric theorems?

**Tip**: When working with geometric proofs, it’s important to clearly define and justify each step using established theorems and properties.

Given m∠ADE = 60° and m∠CDF = (3x + 15)°. Prove x = 15. What is the missing statement and reason in step 5?

Learn how to solve for x in a geometric proof involving vertical angles m∠ADE = 60° and m∠CDF = (3x + 15)°. This problem explores the congruence of vertical angles and the use of algebra to prove that x = 15. Step-by-step solution included. Suitable for students in Grades 7-10.

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