Question

in the diagram below, ⊙o is circumscribed about quadrilateral abcd. what is the value of x? diagram of cyclic quadrilateral a. 74 b. 104 c. 76 d. 106

Explanation:

Step1: Recall cyclic quadrilateral property

In a cyclic quadrilateral (a quadrilateral inscribed in a circle), the sum of opposite angles is \(180^\circ\). So, \(\angle B + \angle D = 180^\circ\).

Step2: Substitute given angle and solve for \(x\)

Given \(\angle B = 94^\circ\) and \(\angle D=x - 12\). Then \(94+(x - 12)=180\).
Simplify: \(x+82 = 180\).
Subtract 82 from both sides: \(x=180 - 82=106\).

Answer:

D. 106