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To find the angle measures, we start by setting up an equation based on the fact that \(\angle 1\) and \(\angle 2\) are supplementary. This means their sum equals \(180^\circ\).

Given:
\[
m \angle 1 = 5x^\circ
\]
\[
m \angle 2 = (x - 6)^\circ
\]

Since \(\angle 1 + \angle 2 = 180^\circ\), we can write the equation:

\[
5x + (x - 6) = 180
\]

### Step 1: Simplify the Equation
Combine like terms:
\[
6x - 6 = 180
\]

### Step 2: Solve for \(x\)
Add 6 to both sides:
\[
6x = 186
\]

Now, divide by 6:
\[
x = 31
\]

### Step 3: Find \(m \angle 1\) and \(m \angle 2\)
1. Substitute \(x = 31\) into \(m \angle 1\):
   \[
   m \angle 1 = 5x = 5(31) = 155^\circ
   \]

2. Substitute \(x = 31\) into \(m \angle 2\):
   \[
   m \angle 2 = x - 6 = 31 - 6 = 25^\circ
   \]

### Final Answer:
\[
m \angle 1 = 155^\circ
\]
\[
m \angle 2 = 25^\circ
\]

Would you like further explanation on any part of this solution?

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Here are some related questions for practice:
1. If two angles are complementary, what would their sum be?
2. How would you solve for \(x\) if the equation was \(4x + (x + 10) = 90\)?
3. What is the value of \(x\) if \(7x + (x - 5) = 180\)?
4. If the measure of \(\angle 1\) is known, how can you find \(\angle 2\) in supplementary pairs?
5. How do you verify that two angles are supplementary?

**Tip:** Remember that supplementary angles always add up to \(180^\circ\).

In the figure below, m∠1 = 5x° and m∠2 = (x - 6)°. Find the angle measures.

Learn how to find the angle measures of supplementary angles where m∠1 = 5x° and m∠2 = (x - 6)°. This problem covers key algebra and geometry concepts, including solving linear equations for angle measures, suitable for students in Grades 7-9.

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