The value of measure of arc FE is 25°.
What is a circle?
A circle is a collection of all points in a plane which are at a constant distance from a fixed point. A circle is a round-shaped figure that has no corners or edges.
For the given situation,
In the figure, GB and GD are the secants of the circle.
In circle, intercept two arcs such that the measure of the angle that the segments form is equal to one-half the difference of the measures of the intercepted arcs. Thus arc length can be found as
[tex]\frac{1}{2}(mBD-mFE)=m \angle BGD[/tex] -------- (1)
Here, BD = [tex]35+100[/tex]
⇒ [tex]135[/tex]
FE = [tex]x[/tex]
m∠BGD = 55°
Now, equation 1 becomes
⇒ [tex]\frac{1}{2}(135-x)=55[/tex]
⇒ [tex](135-x)=55(2)[/tex]
⇒ [tex]135-x=110[/tex]
⇒ [tex]x=135-110[/tex]
⇒ [tex]x=25[/tex]
Hence we can conclude that the value of measure of arc FE is 25°.
Learn more about circles here
https://brainly.com/question/2768531
#SPJ2
