Answer:
m arc DC=48°
Step-by-step explanation:
Angles in a Circle
We know [tex]\overline{BE}[/tex] and [tex]\overline{AC}[/tex] are diameters, so
[tex]m\angle BFA+m\angle AFE=180^o[/tex].
Since [tex]m\angle AFE=3x+12[/tex] and [tex]m\angle BFA=4x[/tex]
We set the equation
[tex]3x+12+4x=180^o[/tex]
Solving
[tex]7x=180-12=168[/tex]
[tex]x=24^o[/tex]
Thus
[tex]m\angle BFA=4(24)=96^o[/tex]
We also know
[tex]m\angle CFD\cong m\angle DFE[/tex]
Being [tex]\angle CFE[/tex] opposite to [tex]\angle BFA[/tex]
Then [tex]m\angle CFE=96^o[/tex]
It's divided in two equal angles [tex]\angle CFD\ and\ \angle DFE[/tex], thus m arc DC is half of 96°:
m arc DC=48°
First option
