Question

a pair of parallel lines is cut by a transversal, as shown in the figure:
which of the following best represents the relationship between angles p and q?
$p = 180$ degrees $- q$
$q = 180$ degrees $- p$
$p = 2q$
$p = q$

Explanation:

Step1: Identify angle relationships

First, recognize that the vertical angle of \( q \) is corresponding to \( p \). Corresponding angles for parallel lines cut by a transversal are equal, so the vertical angle of \( q \) equals \( p \).

Step2: Use vertical angle property

Vertical angles are congruent, so \( q \) is equal to its vertical angle. Thus, \( p = q \).

Answer:

p = q