Find the value of angle g.

Let's solve the geometry problem step-by-step. 1. Understanding the problem: We have a circle with center O. Points C, F, and S are on the circumference of the circle. We are given that angle \(\angle C = 49^\circ\), and we need to find the measure of angle g, which is \(\angle FOS\). 2. Key concepts: * The angle subtended by an arc at the center of a circle is twice the angle subtended by it at any point on the remaining part of the circle. * Inscribed angle theorem. 3. Applying the concepts: According to the inscribed angle theorem, the angle \(\angle COS\) (inscribed angle) is half the angle \(\angle FOS\) (central angle) that subtends the same arc. $$ \angle FOS = 2 \times \angle FCS $$ Since \(\angle FCS = 49^\circ\), we have: $$ \angle FOS = 2 \times 49^\circ $$ $$ \angle FOS = 98^\circ $$ Therefore, the value of angle g (\(\angle FOS\)) is 98 degrees. Answer: 98°