Question

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

Answer 1

Part 1)
`m<C=98\°`

Part 2)
`m\ arc\ BD=98\°`

Part 3)
`m<E=140\°`

Part 4)
`m\ arc\ BF=140\°`

Part 5)
`m<G=122\°`

Part 6)
`m\ arc\ DF=122\°`

Explanation:

we have

`m\ arc\ BFD=262\°`

`m\ arc\ BDF=220\°`

Part 1) Find m<C

we know that

`m<C=m\ arc\ BD` -----> by central angle

`m\ arc\ BD+m\ arc\ BFD=360\°` -----> complete circle

`m\ arc\ BD=360\°-m\ arc\ BFD`

`m\ arc\ BD=360\°-262\°=98\°`

so

`m<C=98\°`

Part 2) Find the measure of arc BD

`m\ arc\ BD=98\°` -----> see the procedure Part 1)

Part 3) Find m<E

we know that

`m<E=m\ arc\ BF` -----> by central angle

`m\ arc\ BF+m\ arc\ BDF=360\°` -----> complete circle

`m\ arc\ BF=360\°-m\ arc\ BDF`

`m\ arc\ BF=360\°-220\°=140\°`

so

`m<E=140\°`

Part 4) Find the measure of arc BF

`m\ arc\ BF=140\°` -----> see the procedure Part 3)

Part 5) Find m<G

we know that

`m<G=m\ arc\ DF` -----> by central angle

`m\ arc\ BF+m\ arc\ BD+m\ arc\ DF=360\°` -----> complete circle

`140\°+98\°+m\ arc\ DF=360\°`

`m\ arc\ DF=360\°-(140\°+98\°)=122\°`

so

`m<G=122\°`

Part 6) Find the measure of arc DF

`m\ arc\ DF=122\°` ----> see the procedure Part 5)