Krishna
0

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