Question

Circle H is inscribed with quadrilateral D E F G. Angle E is 123 degrees. The measure of arc D E is 73 degrees. What is the measure of arc EF in circle H? 41° 50° 114° 173°

Answer 1

Answer: A)41 Degrees

Explanation:

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Answer 2

41 degrees

Explanation:

step 1

Find the measure of arc DGF

we know that

The inscribed angle is half that of the arc comprising

so

`m\angle E=(1)/(2)[arc\ DGF]`

we have

`m\angle E=123^o`

substitute

`123^o=(1)/(2)[arc\ DGF]`

`arc\ DGF=246^o`

step 2

Find the measure of arc EF

we know that

`arc\ DGF+arc\ DE+arc\ EF=360^o` ----> by complete circle

substitute the given values

`246^o+73^o+arc\ EF=360^o`

`319^o+arc\ EF=360^o`

`arc\ EF=360^o-319^o=41^o`