Question

If the radius of a circle is $r$and the length of the arc subtended by a central angle is also $r$, then the measure of the angle is $1\_\_\_\_\_\_\_$.

Short answer

The solution is radian .

Step-by-step solution

Step 1. Given information 

Radius of a circle is $r$and the length of the arc subtended by a central angle is also $r$.

Step 2. Calculation 

For a circle of radius $1$, the rays of a central angle with measure $1$radian subtend an arc of length $1$. For a circle of radius $3$the rays of a central angle with measure $1$radian subtend an arc of length $3$.

So, if radius of a circle is $r$and the length of the arc subtended by a central angle is also $r$, then the measure of the angle is $1$radian.