Since angle ∠1 and angle ∠2 are adjacent angles that form a resulting angle of 160°, we can set up the equation:
\[ m∠1 + m∠2 = 160° \]
Substituting the expressions for the angles into the equation:
\[ 3x + (2x + 10) = 160 \]
Simplifying the left side:
\[ 3x + 2x + 10 = 160 \]
Combining like terms:
\[ 5x + 10 = 160 \]
Next, we can isolate \(x\) by subtracting 10 from both sides:
\[ 5x = 150 \]
Now, divide both sides by 5:
\[ x = 30 \]
Now that we have the value of \(x\), we can find the measures of angles ∠1 and ∠2.
Calculating \(m∠1\):
\[ m∠1 = 3x = 3(30) = 90° \]
Calculating \(m∠2\):
\[ m∠2 = 2x + 10 = 2(30) + 10 = 60 + 10 = 70° \]
Thus, the measures of the two angles are:
\[ m∠1 = 90°, \quad m∠2 = 70° \]
To summarize:
- \(m∠1 = 90°\)
- \(m∠2 = 70°\)