Question

find the measure in degrees of $\angle 4$ if both pairs of lines are parallel and $m\angle 2 = 47^\circ$.

Explanation:

Step1: Identify corresponding angles

Since both pairs of lines are parallel, \(\angle 2\) and \(\angle 3\) are corresponding angles, so \(m\angle 3 = m\angle 2 = 47^\circ\).

Step2: Identify linear pair

\(\angle 3\) and \(\angle 4\) form a linear pair, so they are supplementary. That means \(m\angle 3 + m\angle 4 = 180^\circ\).

Step3: Solve for \(m\angle 4\)

Substitute \(m\angle 3 = 47^\circ\) into the equation: \(47^\circ + m\angle 4 = 180^\circ\). Then \(m\angle 4 = 180^\circ - 47^\circ = 133^\circ\).

Answer:

\(133^\circ\)