The problem asks what $m(\angle BAF)$ equals when $\angle BAC$ is bisected using a compass. We need to choose from the options: A. $m(\angle BFA)$ B. $m(\angle EAF)$ C. $m(\angle EFA)$ D. $m(\angle BAC)$

1. Problem Description

The problem asks what $m(\angle BAF)$ equals when $\angle BAC$ is bisected using a compass. We need to choose from the options:

A. $m(\angle BFA)$

B. $m(\angle EAF)$

C. $m(\angle EFA)$

D. $m(\angle BAC)$

2. Solution Steps

When an angle is bisected, it is divided into two equal angles.

In this case, $\angle BAC$ is bisected by line $AF$, creating two equal angles: $\angle BAF$ and $\angle FAC$.

Therefore, $m(\angle BAF) = m(\angle FAC)$.

Also, $m(\angle BAC) = m(\angle BAF) + m(\angle FAC)$.

Since $m(\angle BAF) = m(\angle FAC)$, then $m(\angle BAC) = m(\angle BAF) + m(\angle BAF) = 2 \cdot m(\angle BAF)$.

This means $m(\angle BAF) = \frac{1}{2} m(\angle BAC)$.

The question is "what: $m(\angle BAF) = \dots$".

We are looking for what $m(\angle BAF)$ equals.

From the diagram, $m(\angle BAF)=m(\angle FAC)$.

Since $m(\angle BAE) = m(\angle FAC)$, the closest option given is B, $m(\angle EAF)$.

3. Final Answer

B. m(∠EAF)