Question

wy || vp, where rz is a transversal. given m∠rtv = 141° and m∠wxz = 39°, complete the statement. the m∠yxz = because and ∠yxz are. 141°; 39°; ∠rtv; ∠wxz; alternate - interior angles; alternate exterior angles; corresponding angles; vertical angles

Explanation:

Step1: Recall linear - pair property

Angles $\angle WXZ$ and $\angle YXZ$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$.

Step2: Calculate $\angle YXZ$

We know that $m\angle WXZ = 39^{\circ}$. Let $m\angle YXZ=x$. Then $m\angle WXZ + m\angle YXZ=180^{\circ}$, so $x = 180^{\circ}-m\angle WXZ$. Substituting $m\angle WXZ = 39^{\circ}$, we get $x=180 - 39=141^{\circ}$. Also, $\angle RTV$ and $\angle YXZ$ are corresponding angles. Since $\overleftrightarrow{WY}\parallel\overleftrightarrow{VP}$ and $\overleftrightarrow{RZ}$ is a transversal, corresponding angles are congruent. Given $m\angle RTV = 141^{\circ}$, then $m\angle YXZ$ is also $141^{\circ}$ because $\angle RTV$ and $\angle YXZ$ are corresponding angles.

Answer:

The $m\angle YXZ = 141^{\circ}$ because $\angle RTV$ and $\angle YXZ$ are corresponding angles.