Question

Find the measure of the numbered angle.

Answer 1

The angle adjacent to angle 6 is the one we need to find first.  To do this, add the measures of the intercepted arcs and divide by 2.  60 + 50 = 110, and half of that is 55.  That means that both adjacent angles to the angle 6 are 55 (vertical angles are congruent).  The measure of all the angles added together is 360 and angle 6 is vertical to the other "sideways" angle, so they are congruent as well.  360 - 55 - 55 = 250.  Split that up between angle 6 and its vertical angle to get that each of those measure 125.  Angle 6 measures 125, choice b from above.