Answer:
The answer is "[tex]\bold{\frac{2 \pi}{3}}[/tex]"
Step-by-step explanation:
Please find the complete question in the attached file.
Using formula:
[tex]\to \bold{\theta = \frac{S}{r}}[/tex]
Where,
[tex]\theta =central \ angle \\\\{S} = arc \ length\\\\{r} = radius \ length[/tex]
[tex]\to \theta = \frac{PQ }{OQ}[/tex]
[tex]=\frac{6 \pi}{9} \\\\ = \frac{2 \pi}{3}[/tex]
The radian measure of central angle POQ is 3π/4 radians. Option b) is the correct option.
Line segments PO and QO are radii.
We need to find the radian measure of central angle POQ.
[tex]2\pi^c = 360^\circ = \text{Full circumference}[/tex]
The superscript 'c' shows angle measured is in radians.
If the radius of the circle is of r units, then:
[tex]1^c \: \rm covers \: \dfrac{circumference}{2\pi} = \dfrac{2\pi r}{2\pi} = r\\\\or\\\\\theta^c \: covers \:\:\: r \times \theta \: \rm \text{units of arc}[/tex]
We know that
π radians = 180°
Therefore,
180° = π radians
135° = x
180° × x = 135° × π radians
x = 135° × π radians/180
x = 3π/4 radians
Hence, the radian measure of central angle POQ is 3π/4 radians. Option b) is the correct option.
Learn more about angle, arc length relation here:
https://brainly.com/question/15451496
#SPJ5
