Question

look at this diagram:

diagram of lines mo, pr (parallel), and transversal sl intersecting them at n and q, with points p, r on pr; m, o on mo; s, q, n, l on sl

if \\( \overleftrightarrow{mo} \\) and \\( \overleftrightarrow{pr} \\) are parallel lines and \\( m\angle pqs = 110^\circ \\), what is \\( m\angle pqn \\)?

\\( \square^\circ \\)

submit

Explanation:

Step1: Identify angle relationship

∠PQS and ∠PQN are supplementary angles (they form a linear pair), so their measures add up to \(180^\circ\).

Step2: Calculate \(m\angle PQN\)

Given \(m\angle PQS = 110^\circ\), we use the formula \(m\angle PQN = 180^\circ - m\angle PQS\).
Substitute the value: \(m\angle PQN = 180^\circ - 110^\circ = 70^\circ\).

Answer:

\(70\)