CPM Homework Help : CCG Problem 10-104

The radian measure of a central angle of $90º$ is $\frac { \pi } { 2 }$ . What must the radian measure of a central angle of $180º$ be? How can you tell without actually computing the radian measure?

Answer:

Since the angle is doubled, the arc length must be doubled, and in turn, the ratio of arc length to radius, or radian measure, must also double and thus be $π$ .