To find the measures of angles ∠1 and ∠2, we start by setting up the equation based on the given information. The sum of adjacent angles ∠1 and ∠2 is equal to the resulting angle of 135°.
Given:
- m∠1 = (2x)°
- m∠2 = (2x + 7)°
We can set up the equation:
\[ m∠1 + m∠2 = 135° \]
Substituting the expressions for m∠1 and m∠2:
\[ (2x) + (2x + 7) = 135° \]
Combining like terms:
\[ 4x + 7 = 135° \]
Now, we subtract 7 from both sides:
\[ 4x = 135° - 7° \] \[ 4x = 128° \]
Next, we divide both sides by 4 to solve for x:
\[ x = \frac{128°}{4} = 32° \]
Now, we can find the measures of ∠1 and ∠2:
\[ m∠1 = 2x = 2(32°) = 64° \] \[ m∠2 = 2x + 7 = 2(32°) + 7° = 64° + 7° = 71° \]
Thus, the measures of the angles are:
\[ m∠1 = 64° \quad \text{and} \quad m∠2 = 71° \]
Final answer: m∠1 = 64°, m∠2 = 71°