Question

safi, raihana
2025 nshs parallel lines and angles assessme
in the figure below, \\( \overline { p s } \parallel \overline { q r } \\) and \\( \overline { p q } \parallel \overline { s r } \\).
what is \\( m \angle q r s \\)?
\\( 50 ^ { \circ } \\)
\\( 60 ^ { \circ } \\)
\\( 80 ^ { \circ } \\)
\\( 100 ^ { \circ } \\)

Explanation:

Step1: Identify the quadrilateral type

Since \( \overline{PS}\parallel\overline{QR}\) and \( \overline{PQ}\parallel\overline{SR}\), \(PQRS\) is a parallelogram.

Step2: Use the property of consecutive angles in a parallelogram

In a parallelogram, consecutive angles are supplementary. That is, if one angle is \(x\), the consecutive angle is \(180 - x\).
Given one angle \( \angle PQR=80^{\circ}\), and \( \angle QRS\) is consecutive to \( \angle PQR\).
So, \(m\angle QRS = 180^{\circ}-80^{\circ}\)

Answer:

\(100^{\circ}\)