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Part A
A map shows the layout of four city streets. The streets have the following properties:
• North Street, Center Street, and South Street are parallel to each other.
• Main Street intersects the other three streets. Answer the following questions:
1. What is the measure, in degrees, of ∠1? Show or explain how you got your answer.
2. What is the measure, in degrees, of ∠2 ? Show or explain how you got your answer.

3. What is the measure, in degrees, of ∠3? Show or explain how you got your answer.

Part B
Suppose that two additional streets, Elm Street and Oak Street, are added to the map. The streets have the following properties:
• Elm Street is perpendicular to Main Street.
• Elm Street is also perpendicular to Oak Street.
What is the relationship of the lines that represent Main Street and Oak Street? Explain your reasoning.

1. Angle 1 and angle with degree measure of 48° are vertical angles (opposite when two lines intersect). Vertical angles are congruent, so angle 1 has measure of 48°.

2. Angles 1 and 2 are same-side interior angles, they add up to 180°, so

m∠2=180°-m∠1=180°-48°=132°

3. Angles 2 and 3 are alternate exterior angles, they are congruent, so

m∠3=132°

Part B. If Elm Street is perpendicular to Main Street and is also perpendicular to Oak Street, then Main street and Oak Street are parallel.

ewomazinoade ewomazinoade · Answer 2 · 2022-03-31T16:09:57+02:00

The measure of angle 1 is 48°.

The measure of angle 2 is 132°.

The measure of angle 3 is 132°.

What are the measure of the angles?

Angle 1 and angle 48 are vertically opposite angles. Vertically opposite angle have the same values. Thus, angle 1 would be 48.

Angle 1 and 2 are interior opposite angles. Thus, both angles should add up to 180 degrees.

180 - 48 = 132

Angle 2 and 3 are alternate external angles. Thus, they are equal. Angle 3 would be 132.

To learn more about angles, please check: https://brainly.com/question/2766460