Question

quadrilateral abcd is inscribed in circle o, as shown.
what is the value of y?
y =

Explanation:

Step1: Use the property of inscribed quadrilaterals

In a cyclic quadrilateral (a quadrilateral inscribed in a circle), the sum of opposite angles is \(180^{\circ}\).
For quadrilateral \(ABCD\), \(\angle A+\angle C = 180^{\circ}\) and \(\angle B+\angle D=180^{\circ}\).
We are given \(\angle D = 83^{\circ}\) and we need to find \(y\) (where \(y=\angle B\)).

Step2: Apply the formula

Since \(\angle B+\angle D = 180^{\circ}\) (opposite angles of a cyclic quadrilateral), we can write the equation \(y + 83^{\circ}=180^{\circ}\).
To solve for \(y\), we use the subtraction property of equality: \(y=180^{\circ}- 83^{\circ}\).

Answer:

\(y = 97\)