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)

Answer 1

In a cyclic quadrilateral (a quadrilateral inscribed in a circle), the opposite angles are supplementary. This means that the sum of the measures of the opposite angles equals 180°.

Given that we have two consecutive angles measuring 88° and 108°, we can label the angles as follows:

• Let angle A = 88°
• Let angle B = 108°
• Let angle C (opposite A) = x°
• Let angle D (opposite B) = y°

From the properties of cyclic quadrilaterals, we know:

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

Since angle A measures 88°, we can find angle C:

\[ 88° + x° = 180° \] \[ x° = 180° - 88° \] \[ x° = 92° \]

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

\[ \boxed{92} \]