Krishna
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Step 1: Investigate the given figure for the given hints.


Step 2: Recall all the necessary properties of circle and quadrilateral


Step 3: Find the angle in the alternate segment

          NOTE: Alternate Segment theorem:  In any circle, the angle between a

                      chord and a tangent through one of the end points of the chord is

                      equal to the angle in the alternate segment,

          EXAMPLE: So, alternate segment Angle \angleWZX = 53 because

                        the angle between a chord and a tangent is 53


Step 4: Find the opposite angle in the quadrilateral inscribed in a circle.

            NOTE: Opposite angles in any quadrilateral inscribed in a circle are

            supplements of each other.

            EXAMPLE: \angle ZWX + \angle XYZ = 180

                              So, \angle XYZ = 180 - 85

                                     \angle XYZ = 95

        

Step 5: Find the remaining angle in the figure(triangle)  

            NOTE: Sum of angles in a triangle is 180

            EXAMPLE: \angle WXZ = 180 -(85 + 53) = 180 - 138

                                     \angle WXZ = 42

                                 \angle XZY = 180 - (95 + 43) = 180 - 138

                                       \angle XZY  = 42


Step 6: After calculating all the angles, make sure that alternating angles are equal                  

            or not  

            NOTE: If alternating angles are equal then we can say that the two lines are

                        parallel.

            EXAMPLE: Alternating angles \angle WXZ = \angle XZY = 42 So, WX and YZ are parallel lines