Find the measure of x.

Inscribed Quadrilateral Theorem says that quadrilateral can be inscribed in a circle if and only if the opposite angles are supplementary.
That means
∠C+∠A=180⁰
∠B+∠D=180⁰
So, ∠C+∠A=180⁰ ---->84 + x = 180 ------> x=180-84=96⁰.
Answer: x=96⁰.