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