Question

the figure below shows part of a circle, with central angle as marked. what part of the full circle does the figure represent? express your answer as a fraction in simplest terms.

Explanation:

Step1: Recall the total degrees in a circle

A full - circle has \(360^{\circ}\).

Step2: Set up the fraction

The fraction of the circle is \(\frac{\text{central angle}}{\text{total degrees in a circle}}\). Given the central angle \(\theta = 60^{\circ}\), the fraction is \(\frac{60}{360}\).

Step3: Simplify the fraction

Divide both the numerator and the denominator by their greatest common divisor. The GCD of 60 and 360 is 60. \(\frac{60\div60}{360\div60}=\frac{1}{6}\)

Answer:

\(\frac{1}{6}\)