https://r2.erweima.ai/mathbot/image/17244764751119jx5xixp.jpg

The problem asks to find the value of \( X \) for the given angle relationship in the figure.

### Analysis:
The figure shows two adjacent angles with expressions \( 8X - 10 \) and \( 4X - 6 \) representing their measures. Since the angles are adjacent and share a common vertex along a straight line, they form a linear pair. Therefore, their sum should be equal to 180 degrees.

### Set Up the Equation:
\[
(8X - 10) + (4X - 6) = 180
\]

### Combine Like Terms:
\[
8X + 4X - 10 - 6 = 180
\]
\[
12X - 16 = 180
\]

### Solve for \( X \):
Add 16 to both sides:
\[
12X = 196
\]
Divide by 12:
\[
X = \frac{196}{12} = 16.\overline{3}
\]

So, the value of \( X \) is \( 16.\overline{3} \) or approximately \( 16.33 \).

Would you like further details or have any questions? Here are some related questions:

1. What are linear pairs, and why do their angles add up to 180 degrees?
2. How can this method be used to solve for unknown angles in other geometric figures?
3. What happens if the equation setup had an error? How would the solution change?
4. Could the solution process differ if the angles formed another type of geometric configuration?
5. How can \( X \) be used to find the exact angles in the figure?

**Tip:** Always double-check your equation setup when solving for variables in geometry, as small errors can lead to incorrect results.

Learn how to find the value of X in a geometry problem involving adjacent angles forming a linear pair. Step-by-step solution provided with equations and detailed analysis. Suitable for students in Grades 9-12.

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