https://file.aiquickdraw.com/mathbot/file/1730079011183936gyetd.jpg

To solve this problem, let's break down the given information:

1. **Given:**  
   - \(\angle 1\) and \(\angle 2\) form a linear pair.  
   - \( m\angle 1 = 18x - 1 \)  
   - \( m\angle 2 = 23x + 17 \)

2. **Concept:**  
   Since \(\angle 1\) and \(\angle 2\) form a linear pair, their measures add up to 180°:
   \[
   m\angle 1 + m\angle 2 = 180
   \]

3. **Equation Setup:**  
   Substitute the expressions for \( m\angle 1 \) and \( m\angle 2 \) into the equation:
   \[
   (18x - 1) + (23x + 17) = 180
   \]

4. **Combine Like Terms:**
   \[
   18x + 23x - 1 + 17 = 180
   \]
   \[
   41x + 16 = 180
   \]

5. **Solve for \( x \):**
   \[
   41x = 180 - 16
   \]
   \[
   41x = 164
   \]
   \[
   x = \frac{164}{41} = 4
   \]

6. **Find \( m\angle 2 \):**  
   Substitute \( x = 4 \) into the expression for \( m\angle 2 \):
   \[
   m\angle 2 = 23x + 17
   \]
   \[
   m\angle 2 = 23(4) + 17
   \]
   \[
   m\angle 2 = 92 + 17 = 109
   \]

### Answer:
The measure of \( m\angle 2 \) is **109°**.

Would you like further details on this solution, or do you have any questions?

---

### Related Questions
1. What is the measure of \( m\angle 1 \) in this problem?
2. How do we determine if two angles form a linear pair?
3. What properties do linear pairs have in geometry?
4. How would the solution change if the sum of the angles were not 180°?
5. How can we verify if our solution for \( x \) is correct?

### Tip:
For angles in a linear pair, always remember they are supplementary, meaning their measures add up to 180°.

∠1 and ∠2 form a linear pair. If m∠1 = 18x - 1 and m∠2 = 23x + 17, find m∠2.

Learn how to solve for the measure of ∠2 in a linear pair where m∠1 = 18x - 1 and m∠2 = 23x + 17. This problem involves understanding linear pairs and applying algebraic methods to find the solution. 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