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### Problem Analysis:
The angles \( m \angle 1 \) and \( m \angle 2 \) are adjacent angles on a straight line, so their measures add up to \( 180^\circ \).

Given:
- \( m \angle 1 = (x - 16)^\circ \)
- \( m \angle 2 = 6x^\circ \)

Since they are on a straight line:
\[
m \angle 1 + m \angle 2 = 180^\circ
\]

### Solution:
1. Substitute the expressions for \( m \angle 1 \) and \( m \angle 2 \) into the equation:
   \[
   (x - 16) + 6x = 180
   \]

2. Combine like terms:
   \[
   7x - 16 = 180
   \]

3. Add 16 to both sides:
   \[
   7x = 196
   \]

4. Divide by 7:
   \[
   x = 28
   \]

Now, substitute \( x = 28 \) back into the expressions for each angle to find their measures:

- \( m \angle 1 = (x - 16) = 28 - 16 = 12^\circ \)
- \( m \angle 2 = 6x = 6 \times 28 = 168^\circ \)

### Answer:
The measures of the angles are:
- \( m \angle 1 = 12^\circ \)
- \( m \angle 2 = 168^\circ \)

Would you like further details on any part of the solution?

Here are 5 related questions to explore:
1. What if \( m \angle 1 \) were instead given as \( (2x - 20)^\circ \)?
2. How would the problem change if \( m \angle 1 \) and \( m \angle 2 \) were complementary instead of forming a straight line?
3. Can you determine \( x \) if \( m \angle 1 = (x - 10)^\circ \) and \( m \angle 2 = 5x^\circ \)?
4. What are adjacent and supplementary angles, and how do they relate in geometry?
5. How can you use algebra to solve for unknowns in other angle-related problems?

**Tip:** Always remember that adjacent angles on a straight line sum to \( 180^\circ \).

In the figure below, m ∠ 1 = (x − 16)° and m ∠ 2 = 6x°. Find the angle measures.

Learn how to find the measures of angles m ∠ 1 and m ∠ 2 given by (x - 16)° and 6x°, respectively. This problem covers algebra and angle relationships on a straight line, suitable for Grades 7-9.

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