Final answer:
Angle 8, which is the corresponding angle to angle 2, will also have a measure of 36° as they occupy the same relative position on the parallel lines cut by the transversal.
Step-by-step explanation:
To determine the measure of angle 8 in the context of two parallel lines cut by a transversal, it's essential to consider the relationships between the various angles formed. When two parallel lines are intersected by a transversal, alternate interior angles are congruent. In the sketch, if angle 2 is given as 36°, then angle 8, being an alternate interior angle, is also 36°. This is due to the corresponding angles property associated with parallel lines. The alternate interior angle theorem states that when a transversal intersects two parallel lines, the alternate interior angles formed are equal. Therefore, the measure of angle 8 is 36° based on the given information and the properties of angles formed by parallel lines and a transversal.