Circle/Triangle math problem

Question

The question asks to find angles $\angle X$ and $\angle Y$, however I don't know how to do this without assuming that lines $\overline {GO}$ and $\overline{OJ}$ are parallel. The only angle given is $32$ degrees.

Answer 1

Hint: the angle subtended by a chord from a point on a circle is $1/2$ that subtended by the chord from the center of the circle.

$$\angle GOH = 2 \angle GJH$$

Answer 2

$\angle H=90^{\circ}$ is over diameter so $\angle x +32^{\circ}+90^{\circ}=180^{\circ}$ so $$\angle x=58^{\circ}$$ as Americo pointed $$\angle y=180^{\circ}-\angle x=132^{\circ}$$

Answer 3

Hint: See Wikipedia entry: Inscribed angle and show that $$\angle x+\angle y=180^{\circ}.$$

Answer 4

∠JHG=90

∠HJG+∠JHG+∠JGH=180

90+32+x=180

X=58