Question

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

Answer 1

In a cyclic quadrilateral, the sum of opposite angles is always \(180^\circ\).

Let the angles of the quadrilateral be labeled as follows:
- \(A = 88^\circ\) (first angle)
- \(B = 108^\circ\) (second angle)
- \(C = x^\circ\) (opposite to angle \(B\))
- \(D\) (opposite to angle \(A\))

From the property of cyclic quadrilaterals, we can set up the following equations:

1. \(A + C = 180^\circ\)
2. \(B + D = 180^\circ\)

Using the first equation:

\[
88^\circ + x^\circ = 180^\circ
\]

Solving for \(x\):

\[
x^\circ = 180^\circ - 88^\circ = 92^\circ
\]

Thus, the value of \(x\) is:

\[
\boxed{92^\circ}
\]