Question

In circle C, what is mFH? 31° 48° 112° 121°

Answer 1

Got to be 48 degrees if you compare the size to the 38 degree column

Answer 2

we know that

The measurement of the external angle is the semi-difference of the arcs it comprises.

so

Step $1$

Find the measure of the arc AJ

m∠BDE=$\frac{1}{2} *[measure\ arc\ AJ-measure\ arc\ BE]$

in this problem we have

m∠BDE=$37\°$

$measure\ arc\ BE=38\°$

substitute in the formula

$37\°$=$\frac{1}{2} *[measure\ arc\ AJ-38\°]$

$74\°$=$[measure\ arc\ AJ-38\°]$

$measure\ arc\ AJ=74\°+38\°=112\°$

Step $2$

Find the measure of the arc FH

m∠FGH=$\frac{1}{2} *[measure\ arc\ AJ-measure\ arc\ FH]$

in this problem we have

m∠FGH=$32\°$

$measure\ arc\ AJ=112\°$

substitute in the formula

$32\°$=$\frac{1}{2} *[112\°-measure\ arc\ FH]$

$64\°$=$[112\°-measure\ arc\ FH]$

$measure\ arc\ FH=112\°-64\°=48\°$

therefore

the answer is

the measure of the arc FH is $48\°$