two parallel lines, $s$ and $t$, are cut by the transversal $d$ as shown. suppose $m\angle 2 = 140^\circ$.

complete the statements below.

we see that $\angle 2$ and $\angle 3$ are select
and since the lines $s$ and $t$ are parallel, $\angle 2$ and $\angle 3$ are select
so, $m\angle 3 = \quad^\circ$.

we see that $\angle 1$ and $\angle 2$ are select
thus, $\angle 1$ and $\angle 2$ are select
so, $m\angle 1 = \quad^\circ$.

therefore, $\angle 1$ and $\angle 3$ are select
we also see that $\angle 1$ and $\angle 3$ are select

the relationship between $\angle 1$ and $\angle 3$ is an example of the following rule.
when parallel lines are cut by a transversal, select

Question

two parallel lines, $s$ and $t$, are cut by the transversal $d$ as shown. suppose $m\angle 2 = 140^\circ$.

complete the statements below.

we see that $\angle 2$ and $\angle 3$ are select
and since the lines $s$ and $t$ are parallel, $\angle 2$ and $\angle 3$ are select
so, $m\angle 3 = \quad^\circ$.

we see that $\angle 1$ and $\angle 2$ are select
thus, $\angle 1$ and $\angle 2$ are select
so, $m\angle 1 = \quad^\circ$.

therefore, $\angle 1$ and $\angle 3$ are select
we also see that $\angle 1$ and $\angle 3$ are select

the relationship between $\angle 1$ and $\angle 3$ is an example of the following rule.
when parallel lines are cut by a transversal, select

Accepted Answer

# Explanation:

⚡ Using what you learned: lines and angles (parallel, transversal, vertical)

## Step 1: Analyze the relationship between $\angle 2$ and $\angle 3$

* **Relationship type**: $\angle 2$ and $\angle 3$ are on opposite sides of the transversal line $d$ and lie between the two parallel lines $s$ and $t$. This makes them **alternate interior angles**.
* **Property**: Since lines $s$ and $t$ are parallel, alternate interior angles are equal (**congruent**).
* **Calculation**:
  $$
  m\angle 3 = m\angle 2 = 140^\circ
  $$

## Step 2: Analyze the relationship between $\angle 1$ and $\angle 2$

* **Relationship type**: $\angle 1$ and $\angle 2$ lie on a straight line (the transversal line $d$). This makes them **adjacent angles** that form a linear pair.
* **Property**: Angles that form a linear pair are supplementary, meaning their measures add up to $180^\circ$ (**supplementary**).
* **Calculation**:
  $$
  m\angle 1 = 180^\circ - m\angle 2 = 180^\circ - 140^\circ = 40^\circ
  $$

## Step 3: Analyze the relationship between $\angle 1$ and $\angle 3$

* **Relationship type**: $\angle 1$ and $\angle 3$ lie on the same side of the transversal line $d$, with one on the interior and one on the exterior in corresponding positions relative to the parallel lines. This makes them **corresponding angles**.
* **Property**: Since lines $s$ and $t$ are parallel, corresponding angles are equal (**congruent**).
* **General Rule**: When parallel lines are cut by a transversal, **corresponding angles are congruent**.

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# Answer:

* We see that $\angle 2$ and $\angle 3$ are **alternate interior angles**.
* And since the lines $s$ and $t$ are parallel, $\angle 2$ and $\angle 3$ are **congruent**.
* So, $m\angle 3 = 140^\circ$.
* We see that $\angle 1$ and $\angle 2$ are **adjacent angles**.
* Thus, $\angle 1$ and $\angle 2$ are **supplementary**.
* So, $m\angle 1 = 40^\circ$.
* Therefore, $\angle 1$ and $\angle 3$ are **corresponding angles**.
* We also see that $\angle 1$ and $\angle 3$ are **congruent**.
* The relationship between $\angle 1$ and $\angle 3$ is an example of the following rule: When parallel lines are cut by a transversal, **corresponding angles are congruent**.

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QUESTION IMAGE

Question

Explanation:

Step 1: Analyze the relationship between \(\angle 2\) and \(\angle 3\)

Step 2: Analyze the relationship between \(\angle 1\) and \(\angle 2\)

Step 3: Analyze the relationship between \(\angle 1\) and \(\angle 3\)

Answer: