Question

find the value of x. x = ?

Explanation:

Step1: Recall the property of cyclic quadrilaterals

The sum of opposite angles in a cyclic quadrilateral is \(180^{\circ}\).

Step2: Set up the equation

Let \(x\) be the unknown angle. We know that \(x + 104^{\circ}+66^{\circ}+ \text{(the fourth angle)} = 360^{\circ}\). But using the property of cyclic - quadrilaterals (opposite angles sum to \(180^{\circ}\)), we can also use \(x+(104^{\circ}+66^{\circ})= 180^{\circ}\) (since the sum of non - opposite angles in a cyclic quadrilateral is not the key here; actually, for a cyclic quadrilateral \(A + C=B + D = 180^{\circ}\). Let's assume the angles of the cyclic quadrilateral are \(a = 104^{\circ}\), \(b=x\), \(c = 66^{\circ}\), \(d\). Then \(a + c+b + d=360^{\circ}\) and \(a + d=b + c = 180^{\circ}\)).

$$x=180^{\circ}-(104^{\circ}+66^{\circ})$$

Step3: Calculate the value of \(x\)

$$x = 180^{\circ}-170^{\circ}$$

Answer:

\(10\)