https://file.aiquickdraw.com/mathbot/file/1726996655767pc71youo.jpg

The image shows two intersecting lines forming vertical angles with measures \( x \) and \( 5x \). According to the property of vertical angles, they are always equal. Therefore, we can write the equation:

\[
x = 5x
\]

This equation implies \( 1x = 5x \), which isn't possible unless \( x = 0 \). However, since we're dealing with angles, this could suggest that there might be some error in interpretation or setup since \( x \) should generally be greater than 0.

Alternatively, if \( x \) and \( 5x \) are supposed to be supplementary (i.e., they sum up to \( 180^\circ \)), the equation would be:

\[
x + 5x = 180^\circ
\]
\[
6x = 180^\circ
\]
\[
x = 30^\circ
\]

Thus, \( x = 30^\circ \) and \( 5x = 150^\circ \). 

The correct assumption is that these angles are supplementary because they lie on a straight line. 

Would you like more details or have any questions?

### Related Questions:
1. What are vertical angles, and why are they always equal?
2. How do you determine if angles are supplementary?
3. What are complementary angles, and how do they differ from supplementary angles?
4. How can you verify angle relationships in intersecting lines?
5. What happens when more than two lines intersect at a point?

**Tip:** Always check if angles are supplementary or complementary by looking for straight lines or right angles!

Solve for x given that two intersecting lines form vertical angles with measures x and 5x.

Learn how to solve for x when two intersecting lines form vertical angles with measures x and 5x. Explore key geometric concepts like vertical angles and supplementary angles with a detailed step-by-step solution. Suitable for students in Grades 8-10.

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