Question

find the measure of the indicated angle that makes lines u and v parallel.
101°
?
u
v
a. 121°
b. 131°
c. 79°
d. 67°

Explanation:

Step1: Recall the property of consecutive interior angles

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. That is, their sum is \(180^{\circ}\).
Let the unknown angle be \(x\). We know that \(101^{\circ}+x = 180^{\circ}\) (since \(u\parallel v\) and they are consecutive interior angles).

Step2: Solve for \(x\)

Subtract \(101^{\circ}\) from both sides of the equation \(101^{\circ}+x = 180^{\circ}\).
\(x=180^{\circ}- 101^{\circ}\)
\(x = 79^{\circ}\)

Answer:

C. \(79^{\circ}\)