Question

examine the figure below. if the $m\angle4 = 48^{\circ}$, what value is needed for each indicated $\angle$ for the lines to be $||$ and why?
$m\angle6 = $ $48^{\circ}$ by $aia$
$m\angle8 = $ select by select
$m\angle5 = $ $132^{\circ}$ by $consecutive interior angles$

Explanation:

Step1: Identify the relationship between ∠4 and ∠8

∠4 and ∠8 are corresponding angles. When two lines are parallel, corresponding angles are equal.

Step2: Determine the measure of ∠8

Since ∠4 = 48°, and ∠4 and ∠8 are corresponding angles (by the Corresponding Angles Postulate), then \(m\angle8 = 48^{\circ}\)

Answer:

\(m\angle8 = 48^{\circ}\) by Corresponding Angles Postulate