Question

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

Answer 1

Answer:

Part 1) $m$

Part 2) $m\ arc\ BD=98\°$

Part 3) $m$

Part 4) $m\ arc\ BF=140\°$

Part 5) $m$

Part 6) $m\ arc\ DF=122\°$

Step-by-step explanation:

we have

$m\ arc\ BFD=262\°$

$m\ arc\ BDF=220\°$

Part 1) Find m<C

we know that

$m$ -----> 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

$m$

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

$m$ -----> 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

$m$

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

$m$ -----> 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

$m$

Part 6) Find the measure of arc DF

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