Question

What is the value of x if mAB=45 and mCD=42, and how did you get the answer?

Answer 1

When 2 chords intersect, they form 2 pairs of vertical angles.
EACH of these angles is equal to half the sum of the intercepted arcs.
Angle x = .5 * (45 + 42) = .5 * 87
Angle x = 43.5
As to how I got the answer, see attached graphic and this link:
http://www.1728.org/circangl.htm

Answer 2

$\bf \measuredangle x=\cfrac{1}{2}(\widehat{AB}+\widehat{CD})\impliedby \textit{intersecting chords theorem}$