Question

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

a) 0 to π/4 radians
b) π/4 to π/2 radians
c) π/2 to 3xπ/4 radians
d) 3xπ/4 to π radians

Answer 1

To convert 85° to radians, multiply by (π/180). The result is approximately 1.483 radians, which places the central angle's radian measure in the range of π/2 to 3π/4, making option (c) the correct answer.

Step-by-step explanation:

To convert the measure of an arc from degrees to radians, we use the fact that 360 degrees is equivalent to 2π radians. Therefore, to find the radian measure of an 85° arc, we can set up the equation:

85° * (π radians / 180°) = π * 85 / 180 = π * 0.4722...

This calculation results in approximately 1.483 radians, which falls within the range of π/2 to 3π/4 radians (option c).

Since the measure of the central angle in radians is approximately 1.483, which is more than π/2 (about 1.5708) but less than 3π/4 (about 2.3562), the correct answer is option (c).