Question

In F, < CFD = < DFE, m< BFA = 4x, m< AFE = 3x + 12, and BE and AC are diameters.

Answer 1

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