Question

two parallel lines, u and v, are cut by the transversal d as shown. suppose m∠2 = 150°. complete the statements below. we see that ∠2 and ∠3 are vertical angles. and since the lines u and v are parallel, ∠2 and ∠3 are choose one. so, m∠3 = °. we see that ∠1 and ∠2 are choose one. thus, ∠1 and ∠2 are choose one. so, m∠1 = °.

Explanation:

Step1: Recall vertical - angle property

Vertical angles are congruent. Since $\angle2$ and $\angle3$ are vertical angles and $m\angle2 = 150^{\circ}$, then $m\angle3=m\angle2$.

Step2: Determine the measure of $\angle3$

$m\angle3 = 150^{\circ}$

Step3: Identify the relationship between $\angle1$ and $\angle2$

$\angle1$ and $\angle2$ are linear - pair angles. A linear pair of angles is supplementary, meaning the sum of their measures is $180^{\circ}$.

Step4: Calculate the measure of $\angle1$

Let $m\angle1=x$. Then $x + m\angle2=180^{\circ}$. Substitute $m\angle2 = 150^{\circ}$ into the equation: $x+150^{\circ}=180^{\circ}$, so $x=m\angle1=180^{\circ}-150^{\circ}=30^{\circ}$

Answer:

And since the lines $u$ and $v$ are parallel, $\angle2$ and $\angle3$ are congruent. So, $m\angle3 = 150^{\circ}$.
We see that $\angle1$ and $\angle2$ are linear - pair angles. Thus, $\angle1$ and $\angle2$ are supplementary. So, $m\angle1 = 30^{\circ}$.