Question

line n intersects lines p, q, r and s, forming the indicated angles. which two lines are parallel
7.
10/18/24, 9:27 am
geo - unit 2 review quizizz 24/25 | quizizz
a) p and q
b) r and s
c) q and r
d) p and r

Explanation:

Step1: Recall parallel line properties

Parallel lines have equal corresponding angles, alternate - interior angles, and same - side interior angles that are supplementary.

Step2: Analyze angles for each pair

• For \(p\) and \(q\):

The angles formed by transversal \(n\) with \(p\) and \(q\) are not equal in the corresponding or alternate - interior sense. For example, if we consider the angles adjacent to the intersection points, they do not follow the parallel - line angle rules.

• For \(r\) and \(s\):

The angles formed by transversal \(n\) with \(r\) and \(s\) are not equal in the corresponding or alternate - interior sense. For example, \(35^{\circ}\) and \(40^{\circ}\) (adjacent angles in a non - parallel - line intersection sense) do not follow the parallel - line angle rules.

• For \(q\) and \(r\):

The angles formed by transversal \(n\) with \(q\) and \(r\) are not equal in the corresponding or alternate - interior sense.

• For \(p\) and \(r\):

The same - side interior angles: \(130^{\circ}+50^{\circ}=180^{\circ}\) (supplementary). Also, the corresponding angles (if we consider the angle relationships) follow the parallel - line rules. For example, if we use the property that if the sum of same - side interior angles is \(180^{\circ}\), the lines are parallel.

Answer:

d) \(p\) and \(r\)