Step-by-step explanation:
inscribed angles subtended by the same arc are equal.
the central angle of a circle is twice any inscribed angle subtended by the same arc.
the first statement tells us that the 53° angle as well as y stay the same size no matter where on their arcs (between the 2 points connected to O) they would be. so, we don't need to bother with any line lengths.
the 2nd statement tells us that x = 2×53 = 106°. the 53° and x angles refer to the short arc on the right of the 2 points connected to O.
and y and x refer to the larger arc on the left of the 2 line connected to O. that means according to the second statement : 360-x (the big angle around O) = 2y
so,
360 - 106 = 2y
254 = 2y
y = 127°
