https://file.aiquickdraw.com/mathbot/file/1726621998889awsyl1e6.jpg

In the image, we are given two parallel lines, \( m \parallel n \), and a transversal that intersects both lines, forming angles. We are asked to find the value of \( x \).

Here's how we can approach it:

1. The angle labeled as \( 118^\circ \) is given, and it is on one side of the transversal.
2. The angle \( x^\circ \) is on the opposite side of the transversal and inside the parallel lines.

These two angles are **supplementary**, meaning their sum is \( 180^\circ \), because they form a linear pair (they are same-side interior angles due to the parallel lines).

Thus, we can write the equation:
\[
x + 118^\circ = 180^\circ
\]

Solving for \( x \):
\[
x = 180^\circ - 118^\circ = 62^\circ
\]

Therefore, the value of \( x \) is \( 62^\circ \).

Would you like a more detailed explanation or have any further questions?

---

Here are 5 related questions:
1. What are alternate interior angles in parallel line theorems?
2. Can two angles on the same side of a transversal be congruent?
3. What is the difference between corresponding angles and supplementary angles?
4. How do you solve for an unknown angle when both parallel lines and a transversal are involved?
5. What is the definition of a linear pair of angles?

**Tip:** When dealing with parallel lines and transversals, look for angle pairs like corresponding, alternate interior, or supplementary angles to make solving easier.

Learn how to find the value of x in a parallel lines and transversal problem with a given angle of 118°. This solution uses the supplementary angle theorem, demonstrating how angles on the same side of a transversal add up to 180°. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation