A pair of parallel lines is intersected by a transversal such that $\angle 1 $ and $\angle 2 $ form a pair of

Question

A pair of parallel lines is intersected by a transversal such that $\angle 1 $ and $\angle 2 $ form a pair of alternate interior angles. If $ m $\angle 1 $ = 75^\circ $, what is the measure of $\angle 2 $?

Examoogle · Accepted Answer

The correct answer is Option A: $75^\circ$. For any pair of parallel lines cut by a transversal, all alternate interior angles are equal; therefore, if one is 75°, the other must also be 75°.

Step-by-Step Solution & Concepts:
Shortcut Trick: For any pair of parallel lines cut by a transversal, all alternate interior angles are equal; therefore, if one is 75°, the other must also be 75°.

Formula Used: $$\angle 1 = \angle 2$$

Given: Two parallel lines intersected by a transversal. Angle 1 and Angle 2 are alternate interior angles. The measure of angle 1 is 75 degrees.

Steps: Identify Relationship: The problem states that $\angle 1$ and $\angle 2$ are alternate interior angles formed by a transversal intersecting two parallel lines.. Apply Geometric Property: According to the Alternate Interior Angles Theorem, when two parallel lines are cut by a transversal, the alternate interior angles are equal in measure.. Calculate Measure: Given $m\angle 1 = 75^{\circ}$, we substitute this into the equality equation to find $m\angle 2$.

Answer: A is correct because when a transversal intersects two parallel lines, the alternate interior angles are always equal, so the measure of angle 2 is 75°.

Exam Tip: This concept is foundational for solving problems involving polygon angle sums and coordinate geometry slopes where lines are parallel.

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