Answer:
[tex]\text{BF}=80^{\circ}[/tex]
Step-by-step explanation:
We have been given a circle D. Secant BE and CF intersect at point A inside D. We are asked to find the measure of arc BF.
We know that when two secants intersect inside a circle, then the measure of angle formed is half the sum of intercepting arcs.
[tex]m\angle EAF=\frac{\text{Measure of arc EF+Measure of arc BC}}{2}[/tex]
[tex]70^{\circ}=\frac{\text{Measure of arc EF+Measure of arc BC}}{2}[/tex]
[tex]2*70^{\circ}=\frac{\text{Measure of arc EF+Measure of arc BC}}{2}*2[/tex]
[tex]140^{\circ}=\text{Measure of arc EF+Measure of arc BC}[/tex]
We know that degree measure of circumference of circle is 360 degrees, so we can set an equation as:
[tex]\text{Arc EF+BC+EC+BF}=360^{\circ}[/tex]
[tex]140^{\circ}+140^{\circ}+\text{BF}=360^{\circ}[/tex]
[tex]280^{\circ}+\text{BF}=360^{\circ}[/tex]
[tex]280^{\circ}-280^{\circ}+\text{BF}=360^{\circ}-280^{\circ}[/tex]
[tex]\text{BF}=80^{\circ}[/tex]
Therefore, the measure of arc BF is 80 degrees.
