Question

question 22 of 22 in the diagram below, ⊙o is circumscribed about quadrilateral abcd. what is the value of x? a. 117 b. 123

Explanation:

Step1: Recall cyclic - quadrilateral property

Opposite angles of a cyclic quadrilateral are supplementary (sum to 180°). In cyclic quadrilateral \(ABCD\), \(\angle B\) and \(\angle D\) are opposite angles. So, \(\angle B+\angle D = 180^{\circ}\).

Step2: Substitute the given angle measures

We know that \(\angle B = 93^{\circ}\) and \(\angle D=x + 30^{\circ}\). Then, \(93+(x + 30)=180\).

Step3: Simplify the equation

First, combine like - terms: \(x+123 = 180\).

Step4: Solve for \(x\)

Subtract 123 from both sides of the equation: \(x=180 - 123\).

Answer:

\(x = 57\)