Question

which angle has a measure of $46^{circ}$?
$angle pwq$ $angle qwr$ $angle rws$ $angle swt$
vertical angles have the same measure.

Explanation:

Step1: Recall vertical angles property

Vertical angles are formed when two lines intersect. They are opposite each other and have equal measures.

Step2: Identify vertical angle of \(46^{\circ}\)

Looking at the given angles, \(\angle NPW = 46^{\circ}\). The vertical - angle of \(\angle NPW\) is \(\angle RWS\) (since vertical angles are opposite each other at the intersection of two lines).

Answer:

\(\angle RWS\)