Question

look at this diagram:
if ( overleftrightarrow{oq} ) and ( overleftrightarrow{rt} ) are parallel lines and ( mangle rsp = 47^circ ), what is ( mangle qps )?
( square^circ )

Explanation:

Step1: Recall the property of parallel lines

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. Here, \(\overleftrightarrow{QR}\) and \(\overleftrightarrow{RT}\) are parallel lines and \(UN\) is the transversal. So, \(\angle RSP\) and \(\angle QPS\) are consecutive interior angles.

Step2: Use the supplementary - angle formula

If two angles \(\alpha\) and \(\beta\) are supplementary, then \(\alpha+\beta = 180^{\circ}\). Let \(\alpha=\angle RSP = 47^{\circ}\) and \(\beta=\angle QPS\). Then \(m\angle RSP+m\angle QPS=180^{\circ}\).

Step3: Solve for \(m\angle QPS\)

Substitute \(m\angle RSP = 47^{\circ}\) into the equation \(m\angle RSP+m\angle QPS=180^{\circ}\). We get \(47^{\circ}+m\angle QPS = 180^{\circ}\). Then \(m\angle QPS=180^{\circ}- 47^{\circ}\).

Answer:

\(133\)