Given:
Consider the below figure attached with this question.
In circle A below, chord BC and diameter DAE intersect at F.
The arc CD = 46° and arc BE = 78°.
To find:
The measure of angle BFE.
Solution:
According to intersecting chords theorem, if two chords intersect inside the circle then the angle on the intersection is the average of intercepted arcs.
Using intersecting chords theorem, we get
[tex]m\angle BFE=\dfrac{1}{2}(m(arcCD)+m(arcBE))[/tex]
[tex]m\angle BFE=\dfrac{1}{2}(46^\circ+78^\circ)[/tex]
[tex]m\angle BFE=\dfrac{1}{2}(124^\circ)[/tex]
[tex]m\angle BFE=62^\circ[/tex]
Therefore, the measure of angle BFE is 62°.
