Question

1
select the correct answer.
when two parallel lines are cut by a transversal, angles a and b are alternate interior angles that each measure 105°. what is the measure of each of the other alternate interior angles?
○ a. 75°
○ b. 90°
○ c. 105°
○ d. 180°

Explanation:

Step1: Recall the property of alternate - interior angles

When two parallel lines are cut by a transversal, alternate - interior angles are congruent. Also, the sum of adjacent angles (on the same side of the transversal) is \(180^{\circ}\). Let the measure of the other alternate - interior angles be \(x\).
We know that \(105^{\circ}+x = 180^{\circ}\) (because adjacent angles on the same side of the transversal are supplementary).

Step2: Solve for \(x\)

Subtract \(105^{\circ}\) from both sides of the equation \(105^{\circ}+x = 180^{\circ}\).
\(x=180^{\circ}- 105^{\circ}\)
\(x = 75^{\circ}\)

Answer:

A. \(75^{\circ}\)