1. **Problem statement:** Given the diagram with points F, E, D, A, B, C and angles \(\angle CED = 24^\circ\) 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:** EA bisects \(\angle FEB\) means \(\angle FEA = \angle AEB\). 3. EC bisects \(\angle BED\) means \(\angle BEC = \angle CED = 24^\circ\). 4. Since \(\angle CED = 24^\circ\), and EC bisects \(\angle BED\), then \(\angle BEC = 24^\circ\). 5. Given \(\angle BAE = 60^\circ\), and EA bisects \(\angle FEB\), so \(\angle FEA = \angle AEB = 60^\circ\). 6. Using the triangle properties and angle bisector theorem, we can set up equations to find \(x\). 7. Since \(\angle BAE = 60^\circ\), and \(x\) is the angle at B, we find that \(x = 60^\circ\). **Final answer:** \(x = 60^\circ\)