Question

two parallel lines, s and t, are cut by the transversal d as shown. suppose m∠2 = 140°. complete the statements below. we see that ∠2 and ∠3 are choose one and since the lines s and t 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 = °. therefore, ∠1 and ∠3 are choose one we also see that ∠1 and ∠3 are choose one the relationship between ∠1 and ∠3 is an example of the following rule. when parallel lines are cut by a transversal, choose one

Explanation:

Step1: Identify angle - pair relationship for ∠2 and ∠3

∠2 and ∠3 are corresponding angles.

Step2: Use the property of corresponding angles

Since lines s and t are parallel, corresponding angles are congruent. So, \(m\angle3 = m\angle2=140^{\circ}\).

Step3: Identify angle - pair relationship for ∠1 and ∠2

∠1 and ∠2 are linear - pair angles.

Step4: Use the property of linear - pair angles

Linear - pair angles are supplementary. So, \(m\angle1 + m\angle2=180^{\circ}\), then \(m\angle1=180 - m\angle2 = 180 - 140=40^{\circ}\).

Step5: Identify angle - pair relationship for ∠1 and ∠3

∠1 and ∠3 are alternate interior angles.

Step6: State the rule

When parallel lines are cut by a transversal, alternate interior angles are supplementary.

Answer:

We see that ∠2 and ∠3 are corresponding angles.
And since the lines s and t are parallel, ∠2 and ∠3 are congruent. So, \(m\angle3 = 140^{\circ}\).
We see that ∠1 and ∠2 are linear - pair angles.
Thus, ∠1 and ∠2 are supplementary. So, \(m\angle1 = 40^{\circ}\).
Therefore, ∠1 and ∠3 are alternate interior angles.
We also see that ∠1 and ∠3 are supplementary.
The relationship between ∠1 and ∠3 is an example of the following rule.
When parallel lines are cut by a transversal, alternate interior angles are supplementary.