Question

consider the figure shown. classify each of the following statements as always true, sometimes true, or never true.
m∠1 + m∠4 = 180
m∠1 + m∠2 + m∠3 = 180
m∠2 + m∠4 = 180
∠2≅∠3
∠2≅∠4
m∠3 = m∠4
the statement m∠1 + m∠4
sometimes true.
the statement m∠1 + m∠2
never true.
the statement m∠2 + m∠4
always true.
the statement ∠2≅∠3 is

Explanation:

Step1: Recall vertical - angle and linear - pair properties

Vertical angles are equal and linear - pair angles are supplementary.

Step2: Analyze $\angle2$ and $\angle3$

$\angle2$ and $\angle3$ are vertical angles. By the vertical - angle theorem, vertical angles are always equal. So $\angle2\cong\angle3$ is always true.

Answer:

always true