Samantha is studying the geometric design of roads. She uses a surveying tool to measure the angles at the intersections of the roads near to her school, which are shown in the picture below (NOT to scale). Samantha noted that Smith Street is parallel to Abbey Road.

Question



Which of the following statements are true about the picture?  Select three that apply.

A. 

The value of x is 8.

B. 

The value of x is 21.

C. 

The measure of angle A is 42°.

D. 

The measure of angle B is 42°.

E. 

Angles A and B are same side interior angles.

what are the answer

Answer 1

To determine which statements are true, we need to analyze the relationships between the angles created by the parallel lines (Smith Street and Abbey Road) and the transversals intersecting them.

Given that Smith Street is parallel to Abbey Road, we can apply properties of angles formed by parallel lines cut by a transversal:

1. Alternate Interior Angles: These angles are congruent.
2. Corresponding Angles: These angles are also congruent.
3. Same-Side Interior Angles: These angles are supplementary, meaning they add up to 180°.

Assuming that angle A and angle B are given in the problem and they are formed by transversals cutting the parallel streets, we can analyze the statements based on common geometric principles.

Without a specific diagram, I can only hypothesize about angle measurements and relationships. However, I can address the nature of the given statements:

• A. If angle A is known or if angle B is known to be 42°, then the corresponding or alternate angle should logically relate according to the angle rules.

• If angles A and B are described such that they would form same-side interior angles, they cannot both be 42°; thus that statement would be false.

Based on generic geometric relationships, here’s how you would typically evaluate:

1. Measure of A being 42° (assumed): This can support alternate interior or corresponding angles if there is another angle which is congruent and follows through.

2. Measure of B being 42°: This can only be true if Angle B is exactly opposite angle A or is the corresponding angle.

3. x values: The specific numerical value of x depends on other provided angles.

In the absence of values for the angles or additional context in the scenario shared, I encourage you to choose the statements that correspond to true relationships concerning these angles. Typically these would involve the relationships between angles A and B, whether they are equal or supplementary given the parallel lines context.

If you can provide the actual measurements or angles cited in the image, I would provide exact values concerning statements A, B, C, D, and E.