Part 1
[tex]m\angle AOB=m\angle BOC[/tex]
Part 2
Since [tex]m\angle AOB=m\angle BOC[/tex] from part 1, we know that since [tex]m\angle AOB=53^{\circ}[/tex], by the transitive property of equality, [tex]m\angle BOC=53^{\circ}[/tex].
Part 3
[tex]m\angle AOC=m\angle AOB+m\angle BOC=53^{\circ}+53^{\circ}=106^{\circ}[/tex]
