Solve the following circle geometry

Let the vertices of the cyclic quadrilateral be A (top-left), B (top-right), C (bottom-right), and D (bottom-left).

Step 1: Identify the angles and their corresponding arcs.
The angle $f$ is $\angle ADB$. This is an inscribed angle that subtends arc AB.
Therefore, the measure of arc AB is twice the angle $f$:

$$m(\text{arc AB}) = 2f$$

The angle $g$ is $\angle DBC$. This is an inscribed angle that subtends arc DC.
Therefore, the measure of arc DC is twice the angle $g$:

$$m(\text{arc DC}) = 2g$$