https://file.aiquickdraw.com/mathbot/file/17274932084263jsd1gf9.jpg

In this problem, we are given two parallel lines with a transversal intersecting them, and we need to find the value of \( x \). Here’s the process to approach it:

1. **Identify Corresponding Angles:**
   - From the diagram, angle \( 5x + 35^\circ \) (denoted as angle 2) corresponds to the angle labeled as \( 45^\circ \) (denoted as angle 5) because they are alternate interior angles.

2. **Set up an equation:**
   Since alternate interior angles are equal when lines are parallel:
   \[
   5x + 35^\circ = 45^\circ
   \]

3. **Solve for \( x \):**
   Subtract \( 35^\circ \) from both sides:
   \[
   5x = 45^\circ - 35^\circ
   \]
   \[
   5x = 10^\circ
   \]

   Now, divide both sides by 5:
   \[
   x = \frac{10^\circ}{5} = 2^\circ
   \]

Thus, the value of \( x \) is \( \boxed{2^\circ} \).

Would you like more details on alternate interior angles or any other part of this process? 

Here are some related questions for further practice:
1. How are alternate interior angles identified when two parallel lines are intersected by a transversal?
2. If \( x = 2^\circ \), what is the actual measure of the angle labeled \( 5x + 35^\circ \)?
3. What is the relationship between corresponding angles when parallel lines are involved?
4. What other angle relationships exist between parallel lines and a transversal (e.g., supplementary angles)?
5. How would the solution change if the transversal were not perpendicular to the parallel lines?

**Tip:** Always check for congruent angles when solving problems involving parallel lines and transversals.

Find the value of x in the given figure with two parallel lines and a transversal.

Solve for x in a geometry problem involving parallel lines and a transversal. Learn to apply the Alternate Interior Angles Theorem and basic algebra to find that x = 2°. This step-by-step solution is ideal for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation