Answer:
Step-by-step explanation:
All we have to do here is to find the measure of the central angle; the measure of the central angle of a circle is the same measure as the arc it intercepts. Angle DQE in degrees = arc DE in degrees. Use the arc length formula to find the measure of the central angle:
[tex]AL=\frac{\theta}{360}*2 \pi r[/tex] and filling in:
[tex]8.73=\frac{\theta}{360}*(2)(3.14)(10)[/tex] which simplifies to
[tex]8.73=\frac{62.8\theta}{360}[/tex] which simplifies a bit more to
[tex]\frac{360(8.73)}{62.8}=\theta[/tex] so
[tex]\theta=50.04[/tex] degrees. That means that arc DE also measures 50.04 degrees.
