Question

the sketch shows two parallel lines cut by a transversal. angle 2 is 36°. what is the measure of angle 8?

Explanation:

Step1: Identify the relationship between angle 2 and angle 4

Angle 2 and angle 4 are supplementary angles.
$$\angle2+\angle4 = 180^{\circ}$$
$$36^{\circ}+\angle4 = 180^{\circ}$$
$$\angle4=180^{\circ}- 36^{\circ}=144^{\circ}$$

Step2: Identify the relationship between angle 4 and angle 8

Since the two lines are parallel and cut by a transversal, angle 4 and angle 8 are corresponding angles. Corresponding angles are equal.
$$\angle4=\angle8$$

Answer:

$144^{\circ}$