Question

b. in the figure above $\angle 1 = 8x - 11$, $\angle 3 = 2x + 61$, $x = 12$. is $a \parallel v$? choose your answer... how do you know? choose your answer...

Explanation:

Step1: Calculate the measure of ∠1

Substitute \(x = 12\) into the expression for \(\angle1\).
\(\angle1=8x - 11\)
\(\angle1=8\times12-11\)
\(\angle1 = 96 - 11\)
\(\angle1=85^{\circ}\)

Step2: Calculate the measure of ∠3

Substitute \(x = 12\) into the expression for \(\angle3\).
\(\angle3=2x + 61\)
\(\angle3=2\times12 + 61\)
\(\angle3=24 + 61\)
\(\angle3=85^{\circ}\)

Step3: Determine if \(u\parallel v\)

Use the converse of the corresponding angles postulate. If two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel.
Since \(\angle1=\angle3 = 85^{\circ}\), by the converse of the corresponding angles postulate, \(u\parallel v\).

Answer:

Yes, \(u\parallel v\) because \(\angle1 = 8\times12-11=85^{\circ}\) and \(\angle3=2\times12 + 61=85^{\circ}\), and by the converse of the corresponding angles postulate (if corresponding angles are equal, then the lines are parallel).