Question

Find Y *picture in comments*

Answer 1

I am absolutely lost

Answer 2

From a point P on the circle if a tangent PQ is drawn and a chord PR is drawn, then angle RPQ = half the angle of arc PR.

Answer 3

In this problem, yz is a tangent and yx is a chord. The angle between them is the angle marked "y" which is half of the arc formed on the right hand side of yx.
A full circle makes 360 degrees. The arc on the left hand side of yx makes 160 degrees. Therefore, the arc on the right hand side of yx makes 360-160 = 200 degrees.
Therefore angle y = 1/2 * 200 = 100 degrees.

Answer 4

Awesome, thanks for the quick response and explanation. Now what if I was finding z instead? Same diagram.

Answer 5

Angle x = (far arc - near arc) / 2 = (50 - 30) / 2 = 10 degrees.
x + y + z = 180
10 + 100 + z = 180
z = 70 degrees.

Answer 6

Thanks.