Question
The circle has center O, and the measure of angle POQ is 60 degrees. The length of minor arc PQ is what fraction of the circumference of the circle?
(The number of degrees of arc in a circle is 360.)
(The number of degrees of arc in a circle is 360.)
Answers
GPT-4o mini
To find the fraction of the circumference of the circle that the minor arc PQ represents, we need to understand the relationship between the angle at the center of the circle and the arc it subtends.
In this case, the measure of angle POQ is given as 60 degrees. The full angle in a circle is 360 degrees. Therefore, the fraction of the circumference that corresponds to angle POQ can be calculated as follows:
\[
\text{Fraction of arc PQ} = \frac{\text{Measure of angle POQ}}{\text{Total degrees in a circle}} = \frac{60}{360}
\]
Now, we simplify this fraction:
\[
\frac{60}{360} = \frac{1}{6}
\]
Thus, the length of minor arc PQ is \(\frac{1}{6}\) of the circumference of the circle.
Therefore, the answer is \(\boxed{\frac{1}{6}}\).
In this case, the measure of angle POQ is given as 60 degrees. The full angle in a circle is 360 degrees. Therefore, the fraction of the circumference that corresponds to angle POQ can be calculated as follows:
\[
\text{Fraction of arc PQ} = \frac{\text{Measure of angle POQ}}{\text{Total degrees in a circle}} = \frac{60}{360}
\]
Now, we simplify this fraction:
\[
\frac{60}{360} = \frac{1}{6}
\]
Thus, the length of minor arc PQ is \(\frac{1}{6}\) of the circumference of the circle.
Therefore, the answer is \(\boxed{\frac{1}{6}}\).