Question

this angle cuts out \\(\frac{1}{6}\\) of the circle. find the measure of the angle. start by writing \\(\frac{1}{6}\\) as a fraction with a denominator of 360. \\(\frac{1}{6} = \frac{\square}{360}\\) so, the measure of the angle is \\(\square\\) °.

Explanation:

Step1: Find numerator for denominator 360

To convert $\frac{1}{6}$ to a fraction with denominator 360, we find what number multiplied by 6 gives 360. Let that number be $x$. So, $6x = 360$, which means $x=\frac{360}{6}=60$. Then $\frac{1}{6}=\frac{60}{360}$.

Step2: Determine angle measure

A full circle is $360^\circ$. The angle that cuts out $\frac{1}{6}$ of the circle (or $\frac{60}{360}$ of the circle) will have a measure equal to the numerator when the fraction of the circle is $\frac{\text{angle measure}}{360}$. So the angle measure is $60^\circ$.

Answer:

First blank: 60; Angle measure: 60