​Geometry circle question

a.

On this one:

∠A and ∠B are both on the circle and intercept the same arc...so they have the same measure.

∠B = 41º

the third angle in the lower triangle = 180º - (38º + 41º) = 101º

and m∠x = 180º - 101º = 79º

Here's  b

The vertical angle to x  has the same measure....and the endpoints of this angle  have the same endoints  as the inscribed angle having the measure of 15°.....so the arc intercepted by both angles will be 30°

And the measure of the angle formed by 2 chords  that intersect inside the circle is 1/2 the sum of the chords' intercepted arcs. 

So.....x  =   (1/2) (46° + 30°)  =  (1/2) (76°)   =   38°

Here's  c

The vertical angle to the 50° angle will have its endpoints on  arc "x".....since both of these are central angles, then "x"  has the same 50°  measure

And z  is an inscribed angle intercepting this 50° arc....so its measure is (1/2)  of this  = 25°

And using the same intercepting chord theorem as above,   y  =  (1/2)(70° + 50°)  =

(1/2) (120° )   =  60°