Given:
A diagram of a circle O, .
To find:
The measure of arc DC.
Solution:
According to the angle of intersecting chords theorem:
Angle at intersection of chords = Half of the sum of intercepted arcs.
Let be the angle between the intersection of chords AC and BD.
(Linear pair)
Using the angle of intersecting chords theorem, we get
On simplification, we get
Divide both sides by 2.
Now,
Therefore, the correct option is C.