To solve for \( x \), we know that the sum of the two adjacent angles equals the resulting angle of 160°:
\[ m∠1 + m∠2 = 160° \]
Given: \[ m∠1 = 3x° \quad \text{and} \quad m∠2 = (2x + 10)° \]
We can substitute these expressions into the equation:
\[ 3x + (2x + 10) = 160 \]
Now, combine like terms:
\[ 3x + 2x + 10 = 160 \]
\[ 5x + 10 = 160 \]
Next, subtract 10 from both sides:
\[ 5x = 150 \]
Now, divide by 5:
\[ x = 30 \]
Now that we have \( x \), we can find the measures of the two angles:
\[ m∠1 = 3x = 3(30) = 90° \]
\[ m∠2 = 2x + 10 = 2(30) + 10 = 60 + 10 = 70° \]
Thus, the measurements of the two angles are:
\[ m∠1 = 90° \quad \text{and} \quad m∠2 = 70° \]
To summarize:
- \( m∠1 = 90° \)
- \( m∠2 = 70° \)