Question

which angle has a measure of 46°? ∠pwq ∠qwr ∠rws ∠swt

Explanation:

Step1: Identify vertical angles

Vertical angles are congruent (equal in measure). The given $46^\circ$ angle is $\angle NWP$. Its vertical angle is $\angle SWT$.

Step2: Verify right angle check

$\angle NWQ$ is a right angle ($90^\circ$), so $\angle PWQ = 90^\circ - 46^\circ = 44^\circ$. $\angle QWR$ would be supplementary to $\angle PWQ$ (not $46^\circ$), and $\angle RWS$ is vertical to $\angle PWQ$ (so $44^\circ$). Only $\angle SWT$ matches the $46^\circ$ measure.

Answer:

$\angle SWT$