step 1
Find the circumference of the circle
[tex]C=2\cdot\pi\cdot r[/tex]
we have
r=7 yd
substitute
[tex]\begin{gathered} C=2\cdot\pi\cdot7 \\ C=14\pi\text{ yd} \end{gathered}[/tex]
step 2
Remember that the length of the circumference subtends a central angle of 2pi radians
so
Applying proportion
Find out the measure of the central angle for an arc of 7pi yards long
[tex]\frac{2\pi}{14\pi}=\frac{x}{7\pi}[/tex]
solve for x
x=pi radians
