Question

look at this diagram: diagram if $overleftrightarrow{oq}$ and $overleftrightarrow{rt}$ are parallel lines and $mangle ops = 68^circ$, what is $mangle rsp$?

Explanation:

Step1: Identify angle relationship

Since \( \overleftrightarrow{OQ} \parallel \overleftrightarrow{RT} \) and \( \overleftrightarrow{UN} \) is a transversal, \( \angle OPS \) and \( \angle RSP \) are same - side interior angles. The sum of same - side interior angles is \( 180^{\circ} \).

Step2: Calculate \( m\angle RSP \)

We know that \( m\angle OPS = 68^{\circ} \) and \( m\angle OPS+m\angle RSP = 180^{\circ} \). So we can solve for \( m\angle RSP \) by the formula \( m\angle RSP=180^{\circ}-m\angle OPS \).
Substitute \( m\angle OPS = 68^{\circ} \) into the formula: \( m\angle RSP = 180^{\circ}- 68^{\circ}=112^{\circ} \).

Answer:

\( 112 \)