Question

look at this diagram: if (overleftrightarrow{tv}) and (overleftrightarrow{wy}) are parallel lines and (mangle wxu = 65^{circ}), what is (mangle yxz)?

Explanation:

Step1: Note linear - pair relationship

$\angle WXU$ and $\angle YXZ$ form a linear - pair.

Step2: Recall linear - pair property

The sum of angles in a linear - pair is $180^{\circ}$. So, $m\angle WXU + m\angle YXZ=180^{\circ}$.

Step3: Solve for $m\angle YXZ$

Given $m\angle WXU = 65^{\circ}$, then $m\angle YXZ=180^{\circ}-m\angle WXU$. Substitute $m\angle WXU = 65^{\circ}$ into the equation: $m\angle YXZ = 180 - 65=115^{\circ}$.

Answer:

$115$