Circle theorem

Angle x = 100 25 200( 100, 25, 200 ) because angles at the center of a circle are double that at the circumference are half that at the circumference are the same at the circumference( are double that at the circumference, are half that at the circumference, are the same at the circumference ).
Also y = 80 40 160( 80, 40, 160 ) for the same reason because angles in a cyclic quadrilateral because angles in a triangle add to 180( for the same reason, because angles in a cyclic quadrilateral, because angles in a triangle add to 180 ).

O is the centre of a circle
Angle STU = 90 45 60( 90, 45, 60 ),
Angle z = 59 89 104( 59, 89, 104 ),
because the angle in a semicircle is 90 angles in a triangle add to 180 Half a cyclic quadrilateral is 90( the angle in a semicircle is 90, angles in a triangle add to 180, Half a cyclic quadrilateral is 90 )