To solve for \( x \), we start by using the information given about the angles. We know that the two adjacent angles \( \angle 1 \) and \( \angle 2 \) add up to \( 160^\circ \):
\[ m∠1 + m∠2 = 160° \]
Substituting the expressions given for the angles:
\[ 3x + (2x + 10) = 160 \]
Now, combine the terms:
\[ 3x + 2x + 10 = 160 \] \[ 5x + 10 = 160 \]
Next, subtract \( 10 \) from both sides:
\[ 5x = 150 \]
Now, divide both sides by \( 5 \):
\[ x = 30 \]
Now we can find the measures of \( m∠1 \) 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 measures of the angles are:
\[ m∠1 = 90° \quad \text{and} \quad m∠2 = 70° \]
So the final answers are:
\[ m∠1 = 90° , \quad m∠2 = 70° \]
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