we know that
1) the inscribed angle measures half of the arc it comprises.
so
m∠dgf=
> expression ![1](/tex.php?f= 1 )
2) the opposite angles in an inscribed quadrilateral are supplementary angles
so
m∠dgf=![180-123](/tex.php?f= 180-123 )
m∠dgf=
°
substitute in the expression
to find the value of arc ef
![57= \frac{1}{2} (arc\ de+arc\ ef)](/tex.php?f= 57= \frac{1}{2} (arc\ de+arc\ ef) )
![114= (73+arc\ ef) \\ arc\ ef=114-73\\ arc\ ef=41](/tex.php?f= 114= (73+arc\ ef) \\ arc\ ef=114-73\\ arc\ ef=41 )
therefore
the answer is
the measure of the arc ef is ![41\ degrees](/tex.php?f= 41\ degrees )
![What is the measure of arc ef in circle h?](/tpl/images/04/03/XYS90Qjspw5UlplN.jpg)