1. The problem is to find the measures of \( m \angle AEB \), \( m BC \), and \( m \angle AED \) based on the given circle with center E and arcs: AB = 90°, CD = 40°, DA = 108°, and BC unlabeled. 2. Since \( E \) is the center, \( \angle AEB \) is a central angle that intercepts arc AB. By definition, a central angle's measure equals the arc it intercepts. So, \( m \angle AEB = m \overset{\frown}{AB} = 90^\circ \). 3. To find \( m BC \), note the circle's total circumference is 360°. Sum the given arcs: \( 90 + 40 + 108 = 238^\circ \). Thus, \( m \overset{\frown}{BC} = 360^\circ - 238^\circ = 122^\circ \). 4. For \( m \angle AED \), this is the central angle intercepting arc AD. The measure of \( \angle AED \) equals the measure of arc AD. Therefore, \( m \angle AED = m \overset{\frown}{AD} = 108^\circ \). Final answers: \( m \angle AEB = 90^\circ \) \( m BC = 122^\circ \) \( m \angle AED = 108^\circ \)