Mathematics

The key insight is the inscribed angle theorem: an angle inscribed in a circle (vertex on the circle, sides as chords) is always half the central angle that subtends the same arc. Here, the central angle $\angle AOB = 130°$ subtends the minor arc $AB$, and point $C$ sits on the major arc. The angle $\angle ACB$ "sees" that same minor arc from the circle's edge, so it must be half the central angle.

The key insight is the inscribed angle theorem: an angle inscribed in a circle (vertex on the circle, sides as chords) is always half the central angle that subtends the same arc. Here, the central angle $\angle AOB = 130°$ subtends the minor arc $AB$, and point $C$ sits on the major arc. The angle $\angle ACB$ "sees" that same minor arc from the circle's edge, so it must be half the central angle.