1. **Stating the problem:** We are given a geometric figure with points F, E, D, A, B, and C. Angles given are $\angle CED = 24^\circ$ and $\angle BAE = 60^\circ$. Lines EA and EC bisect $\angle FEB$ and $\angle BED$ respectively. We need to find the value of $x$. 2. **Understanding the problem:** - Since EA bisects $\angle FEB$, it divides $\angle FEB$ into two equal parts. - Since EC bisects $\angle BED$, it divides $\angle BED$ into two equal parts. 3. **Using angle bisector properties:** - Let $\angle FEB = 2\alpha$, so $\angle FEA = \alpha$ and $\angle AEB = \alpha$. - Let $\angle BED = 2\beta$, so $\angle BEC = \beta$ and $\angle CED = \beta$. 4. **Given $\angle CED = 24^\circ$, so $\beta = 24^\circ$**. 5. **Since $\angle BAE = 60^\circ$, and EA bisects $\angle FEB$, we can relate these angles to find $x$.** 6. **Using triangle properties and angle sums:** - In triangle ABE, $\angle BAE = 60^\circ$. - Using the bisector properties and given angles, we can find $x$. 7. **Calculate $x$:** - Since $x$ is the angle adjacent to $60^\circ$ and $24^\circ$ in the figure, and considering the bisectors, $x = 30^\circ$. **Final answer:** $$x = 30^\circ$$