The alternate segment theorem says that angles BAC and BCE are congruent, so[tex]m\angle BAC=24^\circ[/tex]###Triangle ABC is isosceles, which makes angles ACB and ABC congruent, and the sum of the interior angles of any triangle is 180 degrees, so[tex]m\angle ACB+m\angle ABC+m\angle BAC=180^\circ[/tex][tex]2m\angle ABC+24^\circ=180^\circ[/tex][tex]m\angle ABC=78^\circ[/tex]###The alternate segment theorem also says that angles DCF and CAD are congruent. Angles DCF, ACD, ACB, and BCE are supplementary, so[tex]m\angle DCF+m\angle ACD+m\angle ACB+m\angle BCE=180^\circ[/tex][tex]m\angle DCF=m\angle CAD=49^\circ[/tex]Then[tex]m\angle ADC+m\angle ACD+m\angle CAD=180^\circ[/tex][tex]m\angle ADC=102^\circ[/tex]###The inscribed angle theorem says that angle COB has twice the measure of angle BAC, so[tex]m\angle COB=48^\circ[/tex]