In a cyclic quadrilateral (a quadrilateral inscribed in a circle), the opposite angles are supplementary, meaning that they add up to \(180^\circ\).
Given the two consecutive angles:
- One angle measures \(88^\circ\)
- The angle next to it (consecutive angle) measures \(108^\circ\)
Let’s label the angles of the quadrilateral as follows:
- Angle 1: \(88^\circ\)
- Angle 2: \(108^\circ\)
- Angle 3: \(y^\circ\) (opposite angle to \(88^\circ\))
- Angle 4: (opposite angle to \(108^\circ\)).
Using the property of the cyclic quadrilateral, we know that:
\[ \text{Angle 1} + \text{Angle 3} = 180^\circ \]
Substituting the known value:
\[ 88^\circ + y^\circ = 180^\circ \]
Now, solving for \(y\):
\[ y^\circ = 180^\circ - 88^\circ \] \[ y = 92^\circ \]
Therefore, the value of \(y\) is:
\[ \boxed{92} \]