Question

if the measure of angle 1 is 118 degrees, what is the measure of angle 7?

Explanation:

Step1: Find the measure of angle 3

Since angle 1 and angle 3 are vertical angles, they are equal. But wait, no! Wait, angle 1 and angle 3 are actually supplementary (if we consider the linear pair with angle 2 and angle 3, but no, wait, angle 1 and angle 4 are vertical angles. Wait, no, in the case of parallel lines \(m\) and \(n\) cut by transversal \(p\), angle 1 and angle 5 are corresponding angles. Wait, no, another approach: angle 1 and angle 3 form a linear pair. So \(m\angle1 + m\angle3=180^{\circ}\). Given \(m\angle1 = 118^{\circ}\), then \(m\angle3=180 - 118=62^{\circ}\).

Step2: Use the property of parallel lines

Since \(m\parallel n\) (assumed from the diagram of parallel - like arrows on \(m\) and \(n\)) and \(p\) is a transversal, angle 3 and angle 7 are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal. So \(m\angle7=m\angle3\).

Answer:

\(62^{\circ}\)