To find the measures of the angles \( m\angle 1 \) and \( m\angle 2 \), we start with the information given:
- The sum of the two adjacent angles is \( 135^\circ \).
- The measures of the angles are represented as:
- \( m\angle 1 = (2x)^\circ \)
- \( m\angle 2 = (2x + 7)^\circ \)
We can set up the equation:
\[ m\angle 1 + m\angle 2 = 135^\circ \]
Substituting in the expressions for \( m\angle 1 \) and \( m\angle 2 \):
\[ 2x + (2x + 7) = 135 \]
Now, simplify the left side:
\[ 2x + 2x + 7 = 135 \]
This simplifies to:
\[ 4x + 7 = 135 \]
Next, we isolate \( 4x \) by subtracting \( 7 \) 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:
- For \( m\angle 1 \):
\[ m\angle 1 = 2x = 2(32) = 64^\circ \]
- For \( m\angle 2 \):
\[ m\angle 2 = 2x + 7 = 2(32) + 7 = 64 + 7 = 71^\circ \]
Thus, the measures of the angles are:
\[ m\angle 1 = 64^\circ, \quad m\angle 2 = 71^\circ \]
So the final answer is:
\( m\angle 1 = 64^\circ, \quad m\angle 2 = 71^\circ \)