https://file.aiquickdraw.com/mathbot/file/1733893790467eib06yh4.jpg

Let’s analyze and solve this question step-by-step:

### Information from the problem:
1. **Parallel lines** \( p \parallel r \).
2. Angles given:
   - \( m\angle 3 = (3x + 20)^\circ \)
   - \( m\angle 6 = (6x - 20)^\circ \).

3. **Relationship between \( \angle 3 \) and \( \angle 6 \):**
   Since \( p \parallel r \) and these angles are corresponding angles, they are **equal**.

   \[
   m\angle 3 = m\angle 6
   \]

### Step 1: Set up the equation
\[
3x + 20 = 6x - 20
\]

### Step 2: Solve for \( x \)
\[
3x + 20 = 6x - 20
\]
Subtract \( 3x \) from both sides:
\[
20 = 3x - 20
\]
Add \( 20 \) to both sides:
\[
40 = 3x
\]
Divide by \( 3 \):
\[
x = \frac{40}{3}
\]

### Step 3: Find \( m\angle 6 \)
Substitute \( x = \frac{40}{3} \) into \( m\angle 6 = 6x - 20 \):
\[
m\angle 6 = 6\left(\frac{40}{3}\right) - 20
\]
Simplify:
\[
m\angle 6 = \frac{240}{3} - 20 = 80 - 20 = 60
\]

### Final Answer:
\[
m\angle 6 = 60^\circ
\]

Would you like a detailed explanation of the relationships or further clarification? 

---

### Follow-Up Questions:
1. What are corresponding angles, and why are they equal in this context?
2. Can you explain how parallel lines affect angle relationships?
3. What happens if two angles are supplementary instead of equal?
4. How can you check your solution for \( x \) by substituting into both angles?
5. What are other types of angle pairs created by parallel lines and a transversal?

### Tip:
When dealing with angles formed by parallel lines and transversals, always identify the type of angle pair (e.g., corresponding, alternate interior, or consecutive interior).

If m∠3 = (3x + 20)° and m∠6 = (6x − 20)°, what is the measure of ∠6?

Learn how to find the measure of angle 6 given m∠3 = (3x + 20)° and m∠6 = (6x − 20)° using algebra and the corresponding angles postulate. This problem explores angle relationships formed by parallel lines and transversals, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation