Answer:
Part 1) [tex]m<C=98\°[/tex]
Part 2) [tex]m\ arc\ BD=98\°[/tex]
Part 3) [tex]m<E=140\°[/tex]
Part 4) [tex]m\ arc\ BF=140\°[/tex]
Part 5) [tex]m<G=122\°[/tex]
Part 6) [tex]m\ arc\ DF=122\°[/tex]
Step-by-step explanation:
we have
[tex]m\ arc\ BFD=262\°[/tex]
[tex]m\ arc\ BDF=220\°[/tex]
Part 1) Find m<C
we know that
[tex]m<C=m\ arc\ BD[/tex] -----> by central angle
[tex]m\ arc\ BD+m\ arc\ BFD=360\°[/tex] -----> complete circle
[tex]m\ arc\ BD=360\°-m\ arc\ BFD[/tex]
[tex]m\ arc\ BD=360\°-262\°=98\°[/tex]
so
[tex]m<C=98\°[/tex]
Part 2) Find the measure of arc BD
[tex]m\ arc\ BD=98\°[/tex] -----> see the procedure Part 1)
Part 3) Find m<E
we know that
[tex]m<E=m\ arc\ BF[/tex] -----> by central angle
[tex]m\ arc\ BF+m\ arc\ BDF=360\°[/tex] -----> complete circle
[tex]m\ arc\ BF=360\°-m\ arc\ BDF[/tex]
[tex]m\ arc\ BF=360\°-220\°=140\°[/tex]
so
[tex]m<E=140\°[/tex]
Part 4) Find the measure of arc BF
[tex]m\ arc\ BF=140\°[/tex] -----> see the procedure Part 3)
Part 5) Find m<G
we know that
[tex]m<G=m\ arc\ DF[/tex] -----> by central angle
[tex]m\ arc\ BF+m\ arc\ BD+m\ arc\ DF=360\°[/tex] -----> complete circle
[tex]140\°+98\°+m\ arc\ DF=360\°[/tex]
[tex]m\ arc\ DF=360\°-(140\°+98\°)=122\°[/tex]
so
[tex]m<G=122\°[/tex]
Part 6) Find the measure of arc DF
[tex]m\ arc\ DF=122\°[/tex] ----> see the procedure Part 5)
