What is the value of x?

Step 1: Recall angle theorem/properties of inscribed quadrilaterals in circle.
LINK: https://www.expii.com/t/angle-properties-of-inscribed-quadrilaterals-952
Step 2: Note down the given equations and examine the diagram
Step 3: Identify the suitable theorem/property for the given question.
EXAMPLE: Opposite angles in an inscribed quadrilateral
are supplementary.
[math] \angle L + \angle J = 180\degree
Step 4: Use the theorem/property to find the unknown value.
EXAMPLE: From triangle ABC
\angle L+\angle J\ =180\degree
\left(x+36\right)+\ \left(x+34\right)=180
Step 5: Solve the equation for the x value
EXAMPLE: (2x+36+34)=180
2x=180\ -\ 70
x=\frac{110}{2}
x = 55
Step 6: Substitute the x values in the given equations to know the unknown values.
x + 36 = 55 + 36 = 91 (since x = 55)
x + 34 = 55 + 34 = 89