With reference to the figure match the angles and arcs to their measures

Angle BAC = (180 - 114) degrees = 66 degrees        [angle on a straight line]

Angle OCA = Angle OBA = 90 degrees                     [angle at the point where the tangent and the radius meet]

Thus, the measure of arc BC = (360 - 66 - 90 - 90) degrees = 114 degrees      [sum of interior angles of a quadrilateral]

Angle CDE = (180 - 124) degrees = 56 degrees        [angle on a straight line]

Angle OCD = Angle OED = 90 degrees                     [angle at the point where the tangent and the radius meet]

Thus, the measure of arc CE = (360 - 56 - 90 - 90) degrees = 124 degrees     [sum of interior angles of a quadrilateral]

Given that the measure of arc BC is 114 degrees and the measure of arc CE is 124 degrees, thus the measure of arc BE = (360 - 114 - 124) degrees = 122 degrees                                                      [angle at a point]

Angle OBF = Angle OEF = 90 degrees                     [angle at the point where the tangent and the radius meet]

Thus, angle BFE = (360 - 122 - 90 - 90) degrees = 58 degrees.