Question

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. which of the following statements are true about the picture? select three that apply. the measure of angle b is 42°. the value of x is 21. the measure of angle a is 42°. the value of x is 8. angles a and b are same side interior angles.

Explanation:

Step1: Use property of same - side interior angles

Since Smith Street is parallel to Abbey Road, angles A and B are same - side interior angles, so $(5x + 2)+(16x + 10)=180$.

Step2: Combine like terms

$5x+16x+2 + 10=180$, which simplifies to $21x+12 = 180$.

Step3: Isolate the variable term

Subtract 12 from both sides: $21x=180 - 12$, so $21x=168$.

Step4: Solve for x

Divide both sides by 21: $x=\frac{168}{21}=8$.

Step5: Find the measure of angle A

Substitute $x = 8$ into the expression for angle A: $16x+10=16\times8 + 10=128+10=138$. The measure of angle B is $5x + 2=5\times8+2=40 + 2=42$.

Answer:

The measure of angle B is 42°.
The value of x is 8.
Angles A and B are same side interior angles.