Question

One of the angles in an intersecting line mesures 30

Answer 1

Think of the point, P,  where the lines intersect as the center of a circle.  The four angles with vertex P add up to 360 degrees.  The given angle and its paired vertical angle are both 30 degrees.  So, the other two angles are also vertical angles with sum 300 degrees (so each of them is a 150 degree angle).