To find the measures of the two adjacent angles \( \angle 1 \) and \( \angle 2 \), we can use the information provided in the problem.
Given:
- \( m\angle 1 = 2x \)
- \( m\angle 2 = 2x + 7 \)
- The angles form a resulting angle of \( 135^\circ \).
Since the angles are adjacent, we can write the equation for their sum:
\[ m\angle 1 + m\angle 2 = 135^\circ \]
Substituting the expressions for the angles into the equation:
\[ 2x + (2x + 7) = 135 \]
Now, simplify and solve for \( x \):
\[ 2x + 2x + 7 = 135 \] \[ 4x + 7 = 135 \] \[ 4x = 135 - 7 \] \[ 4x = 128 \] \[ x = 32 \]
Now we can find the measures of each angle:
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For \( m\angle 1 \): \[ m\angle 1 = 2x = 2(32) = 64^\circ \]
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For \( m\angle 2 \): \[ m\angle 2 = 2x + 7 = 2(32) + 7 = 64 + 7 = 71^\circ \]
Therefore, the measures of the angles are: \[ m\angle 1 = 64^\circ \quad \text{and} \quad m\angle 2 = 71^\circ \]
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