Answer:
Part 7) [tex]arc\ AB=60^o[/tex]
Part 8) [tex]arc\ BAC=240^o[/tex]
Part 9) [tex]arc\ BC=120^o[/tex]
Part 10) [tex]arc\ EA=92^o[/tex]
Part 11) [tex]arc\ ECA=268^o[/tex]
Step-by-step explanation:
Part 7) Find the measure of arc AB
we know that
Central angle is the angle that has its vertex in the center of the circumference and the sides are radii of it
[tex]arc\ AB=60^o[/tex] ----> by central angle
Part 8) Find the measure of arc BAC
we know that
[tex]arc\ BAC=arc\ AB+arc\ AC[/tex]
we have that
The segment AC is a diameter
The diameter divide the circle into two equal parts
so
[tex]arc\ AC=180^o[/tex]
and
[tex]arc\ AB=60^o[/tex]
substitute
[tex]arc\ BAC=60^o+180^o=240^o[/tex]
Part 9) Find the measure of arc BC
we know that
The sum of the minor arc plus the major arc is equal to 360 degrees
so
[tex]arc\ BC+arc\ BAC=360^o[/tex]
we have
[tex]arc\ BAC=240^o[/tex] ----> major arc
[tex]arc\ BC[/tex] ----> minor arc
substitute the given value
[tex]arc\ BC+240^o=360^o[/tex]
[tex]arc\ BC=360^o-240^o=120^o[/tex]
Part 10) Find the measure of arc EA
we know that
The measure of arc EA is equal to
[tex]arc\ EA=arc\ EB+arc\ BA[/tex] ----> by addition angles theorem
we have
[tex]arc\ EB=32^o[/tex] ---> by central angle
[tex]arc\ BA=60^o[/tex] ---> by central angle
[tex]arc\ EA=32^o+60^o=92^o[/tex]
Part 11) Find the measure of arc ECA
we know that
The sum of the minor arc plus the major arc is equal to 360 degrees
so
[tex]arc\ ECA+arc\ EA=360^o[/tex]
we have
[tex]arc\ EA=92^o[/tex] ----> minor arc
[tex]arc\ ECA[/tex] ----> major arc
substitute the given value
[tex]arc\ ECA+92^o=360^o[/tex]
[tex]arc\ ECA=360^o-92^o=268^o[/tex]
