Question

a quadrilateral is inscribed in a circle. two consecutive angles measure 88 degrees and 108 degrees. the angle opposite the 88 degree angle is labeled y degrees. find the value of y

Answer 1

In a cyclic quadrilateral (inscribed in a circle), opposite angles sum up to \(180^\circ\).

Let's denote the angles of the quadrilateral as follows:

- \(A = 88^\circ\) (one given angle)
- \(B = 108^\circ\) (the next consecutive angle)
- \(C = y\) (the angle opposite to angle \(A\))
- \(D\) (the angle opposite to angle \(B\))

From the property of cyclic quadrilaterals, we have:
\[
A + C = 180^\circ
\]
Substituting the value of \(A\):
\[
88^\circ + y = 180^\circ
\]

To find \(y\), we can solve the equation:
\[
y = 180^\circ - 88^\circ
\]
\[
y = 92^\circ
\]

Thus, the value of \(y\) is:
\[
\boxed{92}
\]