Question

if $m\angle 1 + m\angle 2 = 180^\circ$ in the figure below, which of the two lines must be parallel? figure with lines a, b, c, d and angles 1, 2 \bigcirc $c \parallel d$ \bigcirc $a \parallel b$ \bigcirc $c \parallel b$ \bigcirc $a \parallel c$ \bigcirc none of the choices are correct.

Explanation:

Step1: Recall Parallel Line Theorem

When two lines are cut by a transversal, if consecutive interior angles are supplementary (sum to \(180^\circ\)), the lines are parallel.

Step2: Identify Angles and Lines

\(\angle 1\) and \(\angle 2\) are consecutive interior angles formed by transversal \(b\) cutting lines \(c\) and \(d\). Since \(m\angle 1 + m\angle 2 = 180^\circ\), by the consecutive interior angles theorem, \(c \parallel d\).

Step3: Evaluate Other Options

• For \(a \parallel b\): Angles related to \(a\) and \(b\) aren't given as supplementary.
• For \(c \parallel b\) or \(a \parallel c\): No theorem supports these with given angle sum.

Answer:

\(c \parallel d\) (Option: \(c\parallel d\))