Question

this angle cuts out \\(\frac{1}{12}\\) of the circle. find the measure of the angle. start by writing \\(\frac{1}{12}\\) as a fraction with a denominator of 360. \\(\frac{1}{12} = \frac{\square}{360}\\) so, the measure of the angle is \\(\square^\circ\\) (accompanied by an image of a circle with a central angle)

Explanation:

Step1: Find equivalent fraction

To write $\frac{1}{12}$ with denominator 360, we find what factor we multiply 12 by to get 360. $360\div12 = 30$. So we multiply numerator and denominator by 30: $\frac{1\times30}{12\times30}=\frac{30}{360}$.

Step2: Interpret the fraction

A full circle is $360^\circ$, so a fraction of $\frac{30}{360}$ of the circle corresponds to an angle of $30^\circ$ (since the angle measure is the numerator when the denominator is 360 for a circle's angle).

Answer:

The measure of the angle is $30^\circ$.