Geometry: Solving for x with Lines Cut by a Transversal

Published on September 28, 2025

Geometry

Learn how to find the value of x using the property of consecutive interior angles formed by parallel lines and a transversal.

Question

The user has provided an image of a math problem involving lines cut by a transversal. I need to find the value of

Step-by-step derivation:

Identify the type of angles: The image shows two parallel lines, and , intersected by a transversal line, . The angles given are and . These two angles are consecutive interior angles (also known as same-side interior angles).
Recall the property of consecutive interior angles: When two parallel lines are cut by a transversal, the consecutive interior angles are supplementary. This means their sum is .
Set up the equation: Based on the property, we can write the equation:
Solve for x:
- Remove the degree symbols for calculation:
- Combine the constant terms:
- Subtract 40 from both sides:
- Divide by 2:
Verify the answer (optional):
- If , then the second angle is .
- The sum of the two angles is , which confirms the property of consecutive interior angles.

The final answer is