https://file.aiquickdraw.com/mathbot/file/1729635158329brow1mvx.jpg

The diagram shows two intersecting lines with angles around point \( H \). The angle labeled \( 86^\circ \) and the angle labeled \( (2x + 8)^\circ \) appear to be supplementary because they are adjacent angles formed by two intersecting lines, meaning their sum should equal \( 180^\circ \).

The equation to solve for \( x \) can be derived from this relationship:

\[
86^\circ + (2x + 8)^\circ = 180^\circ
\]

Now simplify the equation:

\[
86 + 2x + 8 = 180
\]

\[
2x + 94 = 180
\]

This matches the second equation option provided in the image, \( 2x + 94 = 180 \).

### Solving for \( x \):

\[
2x + 94 = 180
\]

Subtract 94 from both sides:

\[
2x = 86
\]

Now, divide by 2:

\[
x = 43
\]

Thus, the value of \( x \) is 43.

Would you like further details or have any questions? 

Here are 5 questions for further exploration:
1. Why do angles formed by intersecting lines often sum to 180 degrees?
2. How can we identify if angles are complementary or supplementary?
3. What would the equation be if the two angles were complementary instead?
4. How can we generalize this type of angle relationship for different diagrams?
5. Can these techniques apply to more complex geometric shapes?

**Tip:** Always check if the angles around a point or on a straight line add up to 180 degrees or form other specific angle relationships like complementary (90 degrees).

Look at the diagram. Which equation can be used to solve for x? Solve for x.

Learn how to solve for x in a geometry problem involving supplementary angles around a point. The problem involves applying the linear pair theorem and solving a simple algebraic equation. Suitable for students in Grades 6-8.

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