Question

i. since a full circumference is 360 times as long as \\( \frac { 1 } { 360 } \\) of its length, an angle measuring \\( 60 ^ { \circ } \\) subtends an arc on any circle centered at its vertex that is: times as large as the circles circumference or preview try again. what does it mean if the angle measures \\( 60 ^ { \circ } \\)? how is this related to the proportion of a circles circumference the angle subtends if the circle is centered at the angles vertex? percent of the circles circumference. preview try again. once you get the previous part completed correctly, how do you turn a ratio comparison into a percentage comparison?

Explanation:

Step1: Find the ratio of the angle to \(360^{\circ}\)

The formula for the ratio of the arc - length subtended by an angle \(\theta\) (in degrees) at the center of a circle to the circumference of the circle is \(\frac{\theta}{360}\). Given \(\theta = 60^{\circ}\), the ratio is \(\frac{60}{360}=\frac{1}{6}\)

Step2: Convert the ratio to a percentage

To convert the ratio \(\frac{1}{6}\) to a percentage, we use the formula \(P=\frac{1}{6}\times100\%\). \(\frac{1}{6}\times100\%=\frac{100}{6}\% \approx 16.67\%\)

Answer:

The first blank: \(\frac{1}{6}\), the second blank: \(16.67\)