https://file.aiquickdraw.com/mathbot/file/172675774812327gvyiak.jpg

To find the measure of \( x \) in the diagram, let's analyze the geometric relationships:

1. In the diagram, the angles form intersecting lines, creating vertical angles and linear pairs.
2. The angle marked \( x \) and the angle \( \frac{x}{2} + 50^\circ \) are vertical angles, so they are equal.

Given this information, we can set up the equation:

\[
x = \frac{x}{2} + 50
\]

Let's solve for \( x \):

1. Subtract \(\frac{x}{2}\) from both sides to isolate \( x \):

\[
x - \frac{x}{2} = 50
\]

2. Simplify the left side:

\[
\frac{2x}{2} - \frac{x}{2} = \frac{x}{2}
\]

So, we have:

\[
\frac{x}{2} = 50
\]

3. Multiply both sides by 2 to solve for \( x \):

\[
x = 100
\]

Thus, the measure of \( x \) is \( 100^\circ \).

Would you like a detailed explanation of any part of the solution, or do you have any questions?

### Related Questions:
1. How do you identify vertical angles in a diagram?
2. What are linear pairs of angles, and how do they relate to intersecting lines?
3. How can you check if your solution to an equation is correct?
4. How do supplementary angles differ from complementary angles?
5. What are other methods to solve problems involving intersecting lines and angles?

### Tip:
Vertical angles are always equal, so when you see intersecting lines forming angles, look for pairs of vertical angles to set up equations for solving unknowns.

Find the measure of x in the given diagram where angles form vertical angles and a linear pair. The angle on the opposite side of x is given as (x/2) + 50 degrees.

Find the measure of x in a geometric diagram involving vertical angles and a linear pair. This step-by-step solution uses the equation x = (x/2) + 50 and applies key geometry theorems, including vertical angles and linear pairs. Suitable for Grades 8-10.

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