Question

In the xy-plane above, o is the center of the circle, and the measure of ∠aob is π a radians. what is the value of a ?

Answer 1

The complete question in the attached figure

we know that
tan ∠AOB=opposite side angle ∠AOB/adjacent side angle ∠AOB
opposite side angle ∠AOB=1
adjacent side angle ∠AOB=√3
angle ∠AOB=pi/a radians
so
tan (pi/a)=1/√3---------> tan (pi/a)=√3/3

we know  that
tan 30°=√3/3
30° is equal to pi/6 radians
and
angle (pi/a) belong to the I quadrant
so
(pi/a)=pi/6
a=6

the answer is
a=6