Answer:
Part 1) [tex]arc\ AB=49^o[/tex]
Part 2) [tex]arc\ ABC=204^o[/tex]
Part 3) [tex]arc\ BAC=156^o[/tex]
Part 4) [tex]arc\ ACB=311^o[/tex]
Step-by-step explanation:
Part 1) Find the measure of arc AB
we know that
[tex]arc\ AB=m\angle AOB[/tex] ----> by central angle
we have
[tex]m\angle AOB=49^o[/tex]
therefore
[tex]arc\ AB=49^o[/tex]
Part 2) Find the measure of arc ABC
we know that
The central angle of complete circle is equal to 360 degrees
so
[tex]arc\ ABC=360^o-107^o-49^o=204^o[/tex]
Part 3) Find the measure of arc BAC
we know that
[tex]arc\ BAC=arc\ BA+arc\ AC[/tex] ----> by angle addition postulate
we have
[tex]arc\ BA=49^o[/tex] ---> by central angle
[tex]arc\ AC=107^o[/tex] ---> by central angle
so
[tex]arc\ BAC=49^o+107^o=156^o[/tex]
Part 4) Find the measure of arc ACB
we know that
The central angle of complete circle is equal to 360 degrees
so
[tex]arc\ ACB=360^o-arc\ AB[/tex]
substitute
[tex]arc\ ACB=360^o-49^o=311^o[/tex]
