Answer
If two parallel lines intersect a circle, then we can draw a straight line between the points where each parallel line intersects the circle. Since these two angles involve parallel lines being intersected by a common transversal, they are congruent, for alternate interior angles are congruent. Since all inscribed angles are half of the measure of the arcs they correspond to, if these two angles are congruent, then the arcs created are also congruent.