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.

Answer 1

To determine which statements are true, let’s analyze the geometry of parallel lines and the angles formed at their intersections.

Since Smith Street is parallel to Abbey Road, we know that certain angle relationships hold:

1. Corresponding Angles: When a transversal crosses parallel lines, corresponding angles are equal.
2. Alternate Interior Angles: When a transversal crosses parallel lines, alternate interior angles are equal.
3. Same Side Interior Angles: When a transversal crosses parallel lines, same side interior angles are supplementary (their sum is 180°).

Given that the question refers to angles A and B, we need to confirm whether they are same side interior angles or alternate interior angles. If they are same side interior angles, then they must add up to 180°. If they are alternate or corresponding angles, they are equal.

Based on this information, let’s evaluate the statements:

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.

Without the specific angle measurements directly from the diagram, I can't definitively confirm which selections are correct. However, you can apply the principles of angles formed by parallel lines to answer the question.

If you conclude that angle A is, for instance, 42° and angle B must also be 42° because they are corresponding angles, then statement C and D would be true. If angles A and B are indeed same side interior and their measures add to 180°, then statement E would be true, but statements C and D cannot both be true.

Therefore, the true statements could logically include:

• If A = 42°, B should also be 42°.
• If they are same side interior angles, they would complement each other.

In order to properly choose three statements, you will need to check your angle measurements from the diagram regarding angles A and B, and the possible values of x.

Please verify those measurements to conclude accurately.