X is a point inside angle A.
From point X, perpendiculars XY and XD are dropped to the angle sides.
From point A, perpendicular AZ is dropped to segment YD.
With this info,
prove angle PAK= angle MAQ
Hello the undertaker
AX is the diameter of a circle through A,D,X and Y (angle in a semicircle is a right-angle).
So angles ADZ and AXY are equal (angles in same segment).
Therefore angle DAZ = XAY (angle sum of triangles DAZ, XAY)
So angle DAX = angle ZAY.
Grandad