https://file.aiquickdraw.com/mathbot/file/1726003273020pakm842x.jpg

The image shows a pair of intersecting lines, forming a set of angles. The two angles we are concerned with are marked as \(9x + 12\) and \(120^\circ\). These two angles appear to be on a straight line, meaning they are supplementary angles, and their sum should equal \(180^\circ\).

We can set up the equation:
\[
9x + 12 + 120 = 180
\]
Now, let's solve for \(x\):

\[
9x + 132 = 180
\]

Subtract 132 from both sides:

\[
9x = 48
\]

Now, divide by 9:

\[
x = \frac{48}{9} = 5.33 \text{ or } \frac{16}{3}
\]

So, \(x = 5.33\).

Would you like further details or clarifications on any steps? 

Here are 5 related questions to explore further:
1. What are supplementary angles and how do they apply in geometry?
2. How do you solve for unknown variables in linear equations?
3. What are some common angle relationships in intersecting lines?
4. Can you explain how the equation \(9x + 12 + 120 = 180\) was formed?
5. What is the importance of correctly identifying angle types (e.g., supplementary, complementary)?

**Tip**: Always check if angles are supplementary, complementary, or vertical when solving for unknowns in geometry.

Solve for x in the equation formed by a pair of intersecting lines, where one angle is 9x + 12 degrees and the other is 120 degrees.

Learn how to solve a supplementary angle problem involving the equation 9x + 12 + 120 = 180. This problem covers algebraic concepts, solving linear equations, and applying the supplementary angle theorem. Suitable for students in Grades 8-10.

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