Question

find ( mangle bfc ).
( mangle bfc=)
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Explanation:

Step1: Identify vertical angles

Vertical angles are equal. $\angle BFC$ and the angle composed of $\angle AFD$ (which is \(90^{\circ}\)) and \(28^{\circ}\) are supplementary.

Step2: Calculate \(m\angle BFC\)

We know that the sum of angles around a point on a straight - line is \(180^{\circ}\). Since \(\angle AFD = 90^{\circ}\) and \(\angle EFD=28^{\circ}\), and \(\angle BFC+\angle AFD+\angle EFD = 180^{\circ}\) (linear - pair relationship).
Substitute the values: \(m\angle BFC=180-(90 + 28)\)

$$m\angle BFC=180 - 118$$

$$m\angle BFC = 62$$

Answer:

\(62\)