To find the measures of the angles ∠1 and ∠2, we start with the information given:
- The resulting angle formed by ∠1 and ∠2 is \( 135° \).
- The measures of the angles are given by: \[ m∠1 = (2x)° \quad \text{and} \quad m∠2 = (2x + 7)° \]
Since ∠1 and ∠2 are adjacent angles that form a resulting angle of \( 135° \), we can write the equation:
\[ m∠1 + m∠2 = 135° \]
Substituting the expressions for \( m∠1 \) and \( m∠2 \):
\[ (2x) + (2x + 7) = 135° \]
Now, simplify the equation:
\[ 2x + 2x + 7 = 135° \] \[ 4x + 7 = 135° \]
Next, subtract 7 from both sides:
\[ 4x = 135° - 7° \] \[ 4x = 128° \]
Now, divide by 4:
\[ x = \frac{128°}{4} = 32° \]
Now that we have \( x \), we can find the measures of the angles.
Calculate \( m∠1 \):
\[ m∠1 = 2x = 2(32°) = 64° \]
Calculate \( m∠2 \):
\[ m∠2 = 2x + 7 = 2(32°) + 7 = 64° + 7° = 71° \]
Thus, the measures of the two angles are:
\[ m∠1 = 64° \quad \text{and} \quad m∠2 = 71° \]
Final answers:
\[ m∠1 = 64° , \quad m∠2 = 71° \]