figure on scale

Question

generally it is well known that angle inscribed by diameter is $90$,but because on GRE figures are not drawn on scale,that why i want to make sure that my assumption about $y$ is $90$ ,generally in some problem,it is always possible to redraw figures so that create different angles and different form,that why i want to be sure that if such kind of figure would be on GRE, i would not make any mistake,,thanks in advance

Answer 1

The answer is indeed, $y = 90^\circ$, since you are given that the angle is inscribed by the diameter. And you note, this is a fairly well know theorem. That is, by Thales Theorem, we know that $y = 90^\circ$.

So in this case, you can rest assured you are given all the information you need, drawn to scale or not.

Answer 2

The angle at the perimeter is half the angle at the centre.

So, the angle at the centre is $180$, and the angle at the perimeter is $90$.

Answer 3

Since the given chord is said to be diameter use the property :

Angle in a semicircle is a right angle $90 ^\circ $

ref : http://www.mathopenref.com/semiinscribed.html