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The image contains the following math problem:

**In the figure below,**
- \( m \angle 1 = 8x^\circ \)
- \( m \angle 2 = (x - 9)^\circ \)

Find the angle measures.

The diagram shows two angles (1 and 2) that are adjacent and likely form a straight line. This means the two angles are **supplementary**, meaning their sum equals \( 180^\circ \).

We can set up the equation for supplementary angles:

\[
m \angle 1 + m \angle 2 = 180^\circ
\]

Substitute the given expressions for \( m \angle 1 \) and \( m \angle 2 \):

\[
8x + (x - 9) = 180
\]

Simplify the equation:

\[
9x - 9 = 180
\]

Add 9 to both sides:

\[
9x = 189
\]

Now, divide by 9:

\[
x = 21
\]

Now that we know \( x = 21 \), substitute it back into the expressions for the angles:

- \( m \angle 1 = 8x = 8 \times 21 = 168^\circ \)
- \( m \angle 2 = x - 9 = 21 - 9 = 12^\circ \)

So, the measures of the angles are:
- \( m \angle 1 = 168^\circ \)
- \( m \angle 2 = 12^\circ \)

Let me know if you have any questions or need further explanation!

Here are 5 related questions to practice:
1. What are complementary angles, and how do they differ from supplementary angles?
2. If two angles are equal and supplementary, what is their measure?
3. How would the problem change if \( m \angle 1 \) was \( 5x \) instead of \( 8x \)?
4. Can angles larger than \( 180^\circ \) be supplementary? Why or why not?
5. If \( m \angle 1 \) was doubled, what would the value of \( x \) be?

**Tip:** Always check if angles form a straight line to determine if they are supplementary!

In the figure below, m∠1 = 8x° and m∠2 = (x - 9)°. Find the angle measures.

Learn how to solve the equation for x when two supplementary angles are given as m∠1 = 8x° and m∠2 = (x - 9)°. This step-by-step solution explains key algebraic concepts and shows how to find the measures of the angles. Suitable for students in Grades 6-8.

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