1 Answer

Rokas · Answer 1 · 2021-12-12T23:00:56+0000

Answer:

m arc DC=48°

Explanation:

Angles in a Circle

We know
$\overline{BE}$ and
$\overline{AC}$ are diameters, so

$m\angle BFA+m\angle AFE=180^o$ .

Since
$m\angle AFE=3x+12$ and
$m\angle BFA=4x$

We set the equation

3x+12+4x=180^o

Solving

7x=180-12=168

x=24^o

Thus

$m\angle BFA=4(24)=96^o$

We also know

$m\angle CFD\cong m\angle DFE$

Being
$\angle CFE$ opposite to
$\angle BFA$

Then
$m\angle CFE=96^o$

It's divided in two equal angles
$\angle CFD\ and\ \angle DFE$ , thus m arc DC is half of 96°:

m arc DC=48°

First option

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