An arc on a circle measures 85°. the measure of the central angle, in radians, is within which range?

We are given

central angle = 85

we get

now, we can change it into radians

For changing it into radians , we will multiply angle by pi/180

Angle in radian is:

now, we can see that

this is between

.............Answer

Step-by-step explanation:

We are given that :

An arc on a circle measures 85°.         (1)

Since the central angle of a circle and the measure of the arc of the circle are equal.

i.e. central angle = measure of the arc

⇒ the central angle =  85°               [ from (1)]

Also , to convert degrees into radian , we apply the formula :-

So ,

⇒

⇒ lies in first quadrant .

Therefore , the range measure of the central angle is

.

OR

.

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