How to find angle measures and segment length

Answer:
The value of x is [tex]186\°[/tex]
Step-by-step explanation:
Part 27) we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses
In this problem
[tex]90\°=\frac{1}{2}[x\°-6\°][/tex]
Solve for x
[tex]180\°=[x\°-6\°][/tex]
[tex]x=180\°+6\°=186\°[/tex]