Question

this angle cuts out \\(\frac{1}{8}\\) of the circle. find the measure of the angle. start by writing \\(\frac{1}{8}\\) as a fraction with a denominator of 360. \\(\frac{1}{8} = \frac{\square}{360}\\) so, the measure of the angle is \\(\square^\circ\\).

Explanation:

Step1: Find numerator for denominator 360

We know that to convert $\frac{1}{8}$ to a fraction with denominator 360, we set up the equation $\frac{1}{8}=\frac{x}{360}$. Cross - multiplying (i.e., $8x = 360\times1$), we solve for $x$ by dividing both sides by 8: $x=\frac{360}{8}=45$. So $\frac{1}{8}=\frac{45}{360}$.

Step2: Determine the angle measure

A full - circle has a measure of $360^{\circ}$. If the angle cuts out $\frac{1}{8}$ of the circle, and we know that $\frac{1}{8}=\frac{45}{360}$, then the measure of the angle is equal to the numerator of the fraction when the denominator is 360 (because the fraction of the circle the angle cuts out is related to the angle measure over $360^{\circ}$). So the angle measure is $45^{\circ}$.

Answer:

First blank: 45; Angle measure: 45