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 given by \(\frac{\text{central angle}}{\text{total degrees in a circle}}\). Here, the central angle is \(108^{\circ}\), so the fraction is \(\frac{108}{360}\).

Step3: Simplify the fraction

Divide both the numerator and the denominator by their greatest common divisor. The GCD of 108 and 360 is 36.
\(\frac{108\div36}{360\div36}=\frac{3}{10}\)

Answer:

\(\frac{3}{10}\)