To determine the measures of the two angles, we first set up an equation based on the information given. We know that:
- \( m\angle 1 = 2x \)
- \( m\angle 2 = 2x + 7 \)
Since angles \( \angle 1 \) and \( \angle 2 \) are adjacent and together form a resulting angle of 135 degrees, we can write the equation:
\[ m\angle 1 + m\angle 2 = 135 \]
Substituting the expressions for \( m\angle 1 \) and \( m\angle 2 \) into this equation:
\[ 2x + (2x + 7) = 135 \]
Now, simplifying the equation:
\[ 2x + 2x + 7 = 135 \]
\[ 4x + 7 = 135 \]
Next, we subtract 7 from both sides:
\[ 4x = 128 \]
Now, divide by 4:
\[ x = 32 \]
Now that we have the value of \( x \), we can find the measures of the angles:
\[ m\angle 1 = 2x = 2(32) = 64 \]
\[ m\angle 2 = 2x + 7 = 2(32) + 7 = 64 + 7 = 71 \]
Thus, the unknown angle measures are:
\[ m\angle 1 = 64, \quad m\angle 2 = 71 \]
Final answers:
- \( m\angle 1 = 64 \)
- \( m\angle 2 = 71 \)