The rule of the arc of a circle is
[tex]L=\frac{x}{360}\times2\times\pi\times r[/tex]
x is the subtended angle of the arc
r is the radius of the circle
Since the arc subtended an angle of measure 85 degrees, then
x = 85
Since the radius of the circle is 23 inches, then
r = 23
Substitute them in the rule above
[tex]\begin{gathered} L=\frac{85}{360}\times2\times\frac{22}{7}\times23 \\ \\ L=34.1 \end{gathered}[/tex]
The length of the arc is 34.1 inches to the nearest tenth
The answer is 34.1 inches
