1. **Problem statement:** We are given a circle with center O and points A, B, C, D, E, F on the circumference. We know the central angle $\angle AOB = 110^\circ$ and an inscribed angle $\angle FAE = 24^\circ$. We need to find the value of $x$ (an angle at point C on the circumference). 2. **Key formula:** The central angle subtending an arc is twice any inscribed angle subtending the same arc. That is, if $\theta$ is the central angle, then the inscribed angle $\alpha$ on the same arc satisfies: $$\theta = 2\alpha$$ 3. **Step to find $x$:** - The central angle $\angle AOB = 110^\circ$ subtends the arc $AB$. - The inscribed angle $x$ at point C also subtends the same arc $AB$. - By the formula, $x = \frac{110^\circ}{2} = 55^\circ$. 4. **Answer:** $$x = 55^\circ$$