In a cyclic quadrilateral, the opposite angles are supplementary, which means that the sum of the measures of the opposite angles equals 180 degrees.
Let the angles of the cyclic quadrilateral be labeled as follows:
- Angle A = 88°
- Angle B = 108°
- Angle C (opposite to angle B) = x°
- Angle D (opposite to angle A) = y°
According to the property of cyclic quadrilaterals:
- Angle A + Angle C = 180°
- Angle B + Angle D = 180°
From this, we can find angle C: \[ 88° + x° = 180° \] To solve for \( x \), we subtract 88° from both sides: \[ x° = 180° - 88° \] \[ x° = 92° \]
Thus, the value of \( x \) is: \[ \boxed{92} \]