Question

what is the value of x?

Explanation:

Step1: Recall cyclic - quadrilateral property

In a cyclic quadrilateral, the sum of opposite angles is 180°. Angle \(R = 90^{\circ}\), and its opposite angle is \(\angle T=x + 48^{\circ}\).

Step2: Set up the equation

We have the equation \(90+(x + 48)=180\).

Step3: Simplify the equation

First, expand the left - hand side: \(90+x+48=180\), which simplifies to \(x + 138=180\).

Step4: Solve for \(x\)

Subtract 138 from both sides of the equation: \(x=180 - 138\).

Answer:

\(x = 42\)