I'm having trouble understanding this Geometry problem.. any help?

Accepted Solution

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<Cwe 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<Ewe 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)