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:

41 degrees

Step-by-step explanation:

step 1

Find the measure of arc DGF

we know that

The inscribed angle is half that of the arc comprising

so

$m\angle E=\frac{1}{2}[arc\ DGF]$

we have

$m\angle E=123^o$

substitute

$123^o=\frac{1}{2}[arc\ DGF]$

$arc\ DGF=246^o$

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

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

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

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

Answer 2

Answer:

A. 41

Step-by-step explanation:

Anyone on Edg 2020