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.

Answer 1

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

Given the angles:

• One angle is \( 88^\circ \).
• The angle adjacent to it is \( 108^\circ \).
• Let \( y \) be the angle opposite to the \( 88^\circ \) angle.

Since \( 88^\circ \) and \( y \) are opposite angles, we have:

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

To find \( y \), we can rearrange the equation:

\[ y = 180^\circ - 88^\circ \]

Calculating that gives:

\[ y = 92^\circ \]

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

\[ \boxed{92} \]