Question

consider the figure shown. classify each of the following statements as always true, sometimes true, or never true.

$m\angle1 + m\angle4 = 180$
$m\angle1 + m\angle2 + m\angle3 = 180$
$m\angle2 + m\angle4 = 180$
$\angle2 \cong \angle3$
$\angle2 \cong \angle4$
$m\angle3 = m\angle4$

the statement $m\angle1 + m\angle4 = 180$ is

Explanation:

Step1: Analyze the relationship between angles

When two lines intersect, the sum of adjacent angles is \(180^{\circ}\). But \(\angle1\) and \(\angle4\) are not adjacent.

Step2: Consider the general case

In a general intersection of two lines (as shown in the figure), \(\angle1\) and \(\angle4\) are not supplementary.

Answer:

never true