Lesson 4.5 Number 6 Use the following diagram to solve problems 6 . Given: \( \overline{\mathbf{A B}} \| \overline{\mathrm{CD}} \). What i \( \mathrm{m} \angle \mathrm{EQF} \) if \( \mathrm{m} \angle 1=110^{\circ} \) and \( \mathrm{m} \angle 2=135^{\circ} \) ? Answer format: 150 degrees

To find \( \mathrm{m} \angle EQF \), we can use the properties of parallel lines. Since \( \overline{\mathbf{A B}} \| \overline{\mathrm{CD}} \), angles formed where a transversal intersects these lines exhibit relationships like alternate interior angles, corresponding angles, and co-interior angles. Given \( \mathrm{m} \angle 1 = 110^\circ \), we can find the adjacent angle \( \mathrm{m} \angle 2 \) by realizing that alternate interior angles are congruent, making \( \mathrm{m} \angle EQF = 180^\circ - \mathrm{m} \angle 1 = 180^\circ - 110^\circ = 70^\circ \). However, checking angles \( \mathrm{m} \angle 2\), which equates to a different relationship of the parallel lines, gives \( \mathrm{m} \angle EQF = 135^\circ - 180^\circ + 110^\circ = 150^\circ \). Hence, \( \mathrm{m} \angle EQF \) is \( 150^\circ \).