Question

A central angle is an angle whose vertex is at center of a circle. Find measure angle ACC

Answer 1

Part 1

$m\angle AOB=m\angle BOC$

Part 2

Since $m\angle AOB=m\angle BOC$ from part 1, we know that since $m\angle AOB=53^{\circ}$, by the transitive property of equality, $m\angle BOC=53^{\circ}$.

Part 3

$m\angle AOC=m\angle AOB+m\angle BOC=53^{\circ}+53^{\circ}=106^{\circ}$