Question

A quadrilateral is inscribed in a circle. Two consecutive angles measure 88° and 108°. The angle opposite the 88° angle is labeled y° . Find the value of y.(1 point)
y=
°

Answer 1

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:

\[
\boxed{92}
\]