In this question, we’re asked to
find the value of 𝑥. And we can see that 𝑥 is the angle
between two chords in our circle. That’s the chord 𝐴𝐵 and the chord
𝐶𝐷. We can recall the following
fact. The angle between two chords in a
circle is one-half the sum of the measures of the arcs opposite the angle. And in our diagram, we’re given the
measures of both of the arcs opposite our angle 𝑥. That’s the arc 𝐴𝐶, which has
measure 73 degrees, and the arc 𝐷𝐵, which has measure 133 degrees. So by applying this result, we must
have that 𝑥 is equal to one-half times 73 degrees plus 133 degrees. We can then evaluate this
expression. 73 plus 133 is 206, and then
one-half of this is 103 degrees.
Therefore, we were able to show
that if 𝑥 is the angle shown in the diagram, 𝑥 is equal to 103 degrees.