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, opposite angles are supplementary. This means that the sum of the measures of the opposite angles is 180°.

Given:
- One angle measures 88°
- The consecutive angle measures 108°
- The angle opposite the 108° angle is \( x \)

Since the angles 108° and \( x \) are opposite each other, we can express this relationship as:

\[
108° + x = 180°
\]

To find \( x \), we can rearrange this equation:

\[
x = 180° - 108°
\]

Now, calculating the value:

\[
x = 72°
\]

Thus, the value of \( x \) is \( \boxed{72} \)°.