The measure of the angle m∠CFB is 51°.
What is angle of intersecting chords theorem?
The angle of intersecting chords theorem states that, If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
For the given situation,
The diagram shows the two chords that are intersected at F.
Let a be the arc ∠AD = 60° and b be the arc ∠CB = 42°
By theorem,
[tex]\theta = \frac{a+b}{2}[/tex]
where a and b are the arc angles.
On substituting the above values,
⇒ [tex]\angle CFB = \frac{60+42}{2}[/tex]
⇒ [tex]\angle CFB = \frac{102}{2}[/tex]
⇒ [tex]\angle CFB = 51[/tex]
Hence we can conclude that the measure of the angle m∠CFB is 51°.
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