Question

correct! the angle subtends an arc that is 5 radius lengths. therefore, the angle measures 5 radians. b. 1/5 radians preview try again. what proportion of the circles circumference is subtended by the angle? how does this help you determine its measure in radians? submit question 1 points possible: 2 unlimited attempts score on last attempt 1 score in gradebook 1 message instructor about this question post this question to forum

Explanation:

Step1: Recall the formula for radian measure

The formula for the radian measure of an angle \(\theta\) is \(\theta=\frac{s}{r}\), where \(s\) is the arc - length and \(r\) is the radius of the circle.

Step2: Analyze the given information

We are given that the arc - length \(s = 5r\) (since the arc is 5 radius lengths). Substituting \(s = 5r\) into the formula \(\theta=\frac{s}{r}\), we get \(\theta=\frac{5r}{r}\).

Step3: Simplify the expression

When we simplify \(\frac{5r}{r}\), the \(r\) terms cancel out (assuming \(r
eq0\), which is valid for a non - degenerate circle). So \(\theta = 5\) radians.

Answer:

\(5\) radians