Since the two angles are adjacent and form a resulting angle of 160°, we can set up the equation:
\[ m∠1 + m∠2 = 160° \]
Substituting in the expressions for the angles:
\[ 3x + (2x + 10) = 160 \]
Now, we can combine like terms:
\[ 3x + 2x + 10 = 160 \]
\[ 5x + 10 = 160 \]
Next, we subtract 10 from both sides:
\[ 5x = 150 \]
Now, divide both sides by 5 to solve for \( x \):
\[ x = 30 \]
Now we can find the measurements of the two angles.
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:
\[ m∠1 = 90° \quad \text{and} \quad m∠2 = 70° \]
To verify, we can check if their sum equals 160°:
\[ 90° + 70° = 160° \]
This confirms our solution is correct. The values are:
- \( m∠1 = 90° \)
- \( m∠2 = 70° \)