Question

question 17 of 25
in the diagram below, ⊙o is circumscribed about quadrilateral abcd. what is the value of x?
a. 117
b. 57
c. 123

Explanation:

Step1: Recall cyclic - quadrilateral property

Opposite angles of a cyclic quadrilateral are supplementary. That is, the sum of opposite angles is 180°. In cyclic quadrilateral \(ABCD\), \(\angle B\) and \(\angle D\) are opposite angles. So, \(93+(x + 30)=180\).

Step2: Solve the equation for \(x\)

First, simplify the left - hand side of the equation: \(93+x + 30=123+x\). Then, we have the equation \(123+x=180\). Subtract 123 from both sides: \(x=180 - 123\).

Answer:

\(x = 57\), so the answer is B. 57