https://file.aiquickdraw.com/mathbot/file/1727356101873puzbysxe.jpg

The image you've provided shows a transversal intersecting two parallel lines. The goal is to solve for \( x \), where the angle on the right side is given as \( (7x - 3)^\circ \), and another angle on the left is \( 81^\circ \).

### Step-by-Step Solution:

1. **Identify Angle Relationships:**
   Since the two lines are parallel and cut by a transversal, the angles formed are either corresponding, alternate interior, or co-interior (consecutive interior) angles. The angle on the left of the transversal is \( 81^\circ \), and the angle on the right is \( (7x - 3)^\circ \).

2. **Use the Property of Co-Interior Angles:**
   The angles \( \angle BHI \) (which is \( 81^\circ \)) and \( \angle HIC \) (which is \( (7x - 3)^\circ \)) are co-interior angles. For parallel lines, co-interior angles sum up to \( 180^\circ \).
   
   Therefore:
   \[
   81^\circ + (7x - 3)^\circ = 180^\circ
   \]

3. **Solve the Equation:**
   \[
   81 + 7x - 3 = 180
   \]
   Simplify:
   \[
   78 + 7x = 180
   \]
   Subtract 78 from both sides:
   \[
   7x = 102
   \]
   Divide by 7:
   \[
   x = \frac{102}{7} = 14.57
   \]

Thus, the value of \( x \) is approximately \( 14.57 \).

Let me know if you'd like more details on this or have any further questions!

### Related Questions:
1. What are alternate interior angles, and how are they used in solving for unknowns?
2. How do corresponding angles behave when two parallel lines are intersected by a transversal?
3. Can you explain the concept of co-interior (consecutive interior) angles in more detail?
4. How would the solution change if the lines were not parallel?
5. How can the properties of parallel lines and transversals be applied to real-world problems?

### Tip:
When working with parallel lines, always look for angle relationships like corresponding, alternate interior, or co-interior angles to find unknown values easily!

Solve for x in the given diagram where two parallel lines are cut by a transversal, and the angles are 81° and (7x - 3)°.

Learn how to solve for x using the co-interior angles theorem when two parallel lines are cut by a transversal. This problem explores geometric concepts and angle relationships, ideal 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