Left Circle.
To find x, we have to use the central angle theorem to find arc CD.
[tex]\text{arc(CD)}=98[/tex]
Then, we use the inscribed angle theorem, which states that the angle is half its arc.
[tex]x=\frac{1}{2}\text{arc(}DC)=\frac{1}{2}\cdot98=49[/tex]
Hence, x is equal to 49°.
Middle Circle.
Using the same theorem, we have
[tex]S=\frac{1}{2}arc(CD)[/tex]
We know that arc CD measures 86° by the central angle theorem
[tex]S=\frac{1}{2}\cdot86=43[/tex]
Hence, angle S measures 43°.
Right Circle.
We know that angle F is equal to 90° because its arc is half the circle.
We also know that arc CF measures 40° by the central angle theorem. So, we can express the following to find E.
[tex]E=\frac{1}{2}\text{arc(}CF\text{)}=\frac{1}{2}\cdot40=20[/tex]
Hence, angle E measures 20°.
