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 interior angles on the same side of the transversal. If $ m$\angle 1$ = 125^\circ $, what is the measure of $\angle 2 $?

Examoogle · Accepted Answer

The correct answer is Option B: 55^\circ. For parallel lines, consecutive interior angles are supplementary (add up to 180°); simply subtract the given angle from 180°.

Step-by-Step Solution & Concepts:
Shortcut Trick: For parallel lines, consecutive interior angles are supplementary (add up to 180°); simply subtract the given angle from 180°.

Formula Used: $$\angle 1 + \angle 2 = 180^{\circ}$$

Given: Two parallel lines intersected by a transversal, angle 1 = 125 degrees, angle 1 and angle 2 are consecutive interior angles.

Steps: Identify the Property: When two parallel lines are cut by a transversal, interior angles on the same side of the transversal are supplementary.. Substitute Known Values: Given $m\angle 1 = 125^{\circ}$, we substitute this into the supplementary angle equation.. Calculate the Result: Solve for $\angle 2$ by subtracting $125^{\circ}$ from $180^{\circ}$.

Answer: B is correct because the sum of interior angles on the same side of a transversal intersecting parallel lines is always 180°, and 180° - 125° = 55°.

Exam Tip: This property of interior angles is fundamental to solving problems in coordinate geometry, specifically when finding slopes or angles of lines in a plane.

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