E\% Lesson 4.5 Number 5 Use the following dogrom to solve the problem, given that \( \overline{A B} \| \overline{C D} \) and fie \( \ell: \) the tronsversel Jusify your onswers using angle relationships in parollel fres Interseaded by a transversal. What is \( \mathrm{m} \angle 1 \) if \( \mathrm{m} \angle 1=11 \mathrm{x}+35 \) and \( \mathrm{m} \angle 4=\mathrm{x}+1 \) ? Answer format: 150 degress

To determine the measure of \( \angle 1 \), let's analyze the given information step by step. ### Given: - \( \overline{AB} \parallel \overline{CD} \) - Line \( \ell \) is a transversal intersecting these parallel lines. - \( \mathrm{m} \angle 1 = 11x + 35 \) - \( \mathrm{m} \angle 4 = x + 1 \) ### Understanding the Angle Relationships: Since \( \overline{AB} \parallel \overline{CD} \) and \( \ell \) is a transversal, angles formed can be related as **same-side interior angles**, which are **supplementary**. This means: \[ \mathrm{m} \angle 1 + \mathrm{m} \angle 4 = 180^\circ \] ### Setting Up the Equation: \[ (11x + 35) + (x + 1) = 180 \] ### Solving for \( x \): \[ 12x + 36 = 180 \] \[ 12x = 180 - 36 \] \[ 12x = 144 \] \[ x = 12 \] ### Calculating \( \mathrm{m} \angle 1 \): \[ \mathrm{m} \angle 1 = 11x + 35 = 11(12) + 35 = 132 + 35 = 167^\circ \] ### Conclusion: There appears to be a discrepancy between the calculated value (167°) and the expected answer format (150°). It's possible that there might be additional information or a different angle relationship intended in the problem. However, based on the provided information and standard angle relationships: **The measure of \( \angle 1 \) is 167 degrees.**