To solve for \( x \) in the problem, we start with the information given about the angles. We know that the sum of the adjacent angles \( m∠1 \) and \( m∠2 \) equals the resulting angle of 160°.
We have:
- \( m∠1 = 3x \)
- \( m∠2 = 2x + 10 \)
The equation can be set up as follows:
\[ m∠1 + m∠2 = 160° \]
Substituting in the expressions for \( m∠1 \) and \( m∠2 \):
\[ 3x + (2x + 10) = 160 \]
Now, we combine like terms:
\[ 3x + 2x + 10 = 160 \]
This simplifies to:
\[ 5x + 10 = 160 \]
Next, we subtract 10 from both sides:
\[ 5x = 150 \]
Now, we divide by 5 to solve for \( x \):
\[ x = 30 \]
Now that we have \( x \), we can find \( m∠1 \) and \( m∠2 \):
- For \( m∠1 \):
\[ m∠1 = 3x = 3(30) = 90° \]
- For \( m∠2 \):
\[ m∠2 = 2x + 10 = 2(30) + 10 = 60 + 10 = 70° \]
Thus, the measurements of the two angles are:
- \( m∠1 = 90° \)
- \( m∠2 = 70° \)
To summarize:
\[ m∠1 = 90°, \quad m∠2 = 70° \]