Question

1. reason in the parking lot shown, all of the lines for the parking spaces should be parallel. if m∠3 = 61, what should m∠1 and m∠2 be? explain.

Explanation:

Step1: Identify angle - angle relationships

Since the parking - space lines are parallel, $\angle3$ and $\angle1$ are corresponding angles. Corresponding angles formed by parallel lines and a transversal are congruent.
$m\angle1=m\angle3$

Step2: Find the measure of $\angle1$

Given $m\angle3 = 61^{\circ}$, so $m\angle1=61^{\circ}$

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

$\angle1$ and $\angle2$ are supplementary angles (they form a linear - pair). The sum of the measures of two supplementary angles is $180^{\circ}$. So $m\angle1 + m\angle2=180^{\circ}$

Step4: Find the measure of $\angle2$

We know $m\angle1 = 61^{\circ}$, then $m\angle2=180^{\circ}-m\angle1$. Substitute $m\angle1 = 61^{\circ}$ into the equation: $m\angle2=180 - 61=119^{\circ}$

Answer:

$m\angle1 = 61^{\circ}$, $m\angle2 = 119^{\circ}$