Answer:
The measurement of a central angle (in degrees) subtended by an arc is [tex]150^{\circ \:}\:\:[/tex].
Step-by-step explanation:
as
[tex]d= 6[/tex] meters
so
[tex]r= 3[/tex] meters
and
[tex]Arc=\frac{5}{2}\pi[/tex] meters
Using the formula
[tex]\:Arc\:=r\:\theta[/tex]
[tex]\:\frac{5}{2}\pi =3\theta[/tex]
[tex]\mathrm{Switch\:sides}[/tex]
[tex]3\theta =\frac{5}{2}\pi \:[/tex]
[tex]\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}[/tex]
[tex]3\theta =\frac{5\pi \:}{2}[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}3[/tex]
[tex]\frac{3\theta \:}{3}=\frac{\frac{5\pi \:}{2}}{3}[/tex]
Simplify
[tex]\theta \:=\frac{5\pi \:}{6}[/tex]
[tex]\theta \:=\frac{5\left(180^{\circ }\right)\:}{6}[/tex]
[tex]\theta \:=150^{\circ \:}\:\:[/tex]
Therefore, the measurement of a central angle (in degrees) subtended by an arc is [tex]150^{\circ \:}\:\:[/tex].
