Question

Arc CD is 1/4 of the circumference of a circle. What is the radian measure of the central angle?

Answer 1

Answer: is the second answer B!

Answer 2

`(\pi)/(2)` radians

Explanation:

We can use the concept of proportion to answer this question.

The arc CD is given to be 1/4 in measure of the circumference of the circle. A complete circle is 360 degrees in measure which in radian measure is 2π

So, the arc which 1/4 in measure of the circumference will make an angle which is 1/4 of the angle of the entire circle.

i.e.

Angle formed by the arc =
`(1)/(4) * 2 \pi =(\pi)/(2)` radians

Therefore, the radian measure of the central angle of arc CD is
`(\pi)/(2)` radians