Explanation:
The diagram and complete question is shown below. The angles ∠Y and 46° are vertical angles because they lie on opposite sides of intersecting lines, then they measure the same:
[tex]\angle Y=46^{\circ}[/tex]
So:
[tex]m\angle WYX=\angle Y=46^{\circ}[/tex]
We know that:
[tex]m\angle WXY=\angle X=71^{\circ} \\ \\ \\ \text{We also know that W,X,Y form a triangle, so:} \\ \\ \\ \angle W + \angle X + \angle Y=180^{\circ} \\ \\ \\ Substituting \ known \ values: \\ \\ \angle W+71^{\circ} +46^{\circ} =180^{\circ} \\ \\ \\ Isolating \ \angle W: \\ \\ \angle W=180^{\circ} -71^{\circ} -46^{\circ} =63^{\circ} \\ \\ Then: \\ \\ m\angle YWX=\angle W=63^{\circ}[/tex]
In conclusion: Correct options are:
[tex]m\angle WYX=46^{\circ} \\ \\ m\angle YWX=63^{\circ}[/tex]
