Question

In the diagram below, DE and EF are tangent to o what is the measure of DGF

Answer 1

I hope this helps you



DGF+153=360


DGF=207

Answer 2

we know that

The inscribed angle measures half that of the arc comprising

in this problem

m∠DGF -----> is a inscribed angle

m∠DGF=
`(1)/(2)(arc\ DF)`

we have

`arc\ DF=153\°`

substitute

m∠DGF=
`(1)/(2)(153\°)=76.5\°`

we know that

`arc\ DGF+arc\ DF=360\°`

Find the measure of arc DGF

`arc\ DGF=360\°-arc\ DF`

`arc\ DGF=360\°-153\°=207\°`

therefore

the answer is

a) the measure of inscribed angle m∠DGF is
`76.5\°`

b) the measure of arc DGF is
`207\°`