Math 11 - Tangent and circle question WITH IMAGE

PQ and PR are tangent to circle O. Write y as a function of x.
O is the center. How do I get the answer?

http://i52.tinypic.com/2wptkpg.jpg

The answer is y = 2x - 180
Thanks!

angle PQO = angle PRO = 90 degrees
angle QOR + y = 180 degres
whence angle QOR = 180 degrees -- y .........(A)
360 degrees -- angle QOR = 2x as it is subtended by the same arc at the centre
angle QOR = 360 degrees -- 2x ...........(B)
equating (B) and (A),
360 -- 2x = 180 -- y
OR y = 2x -- 180

Let a = measure of major arc QR, and b = measure of minor arc QSR.

The measures of arcs QR and QSR add to a full circle, or 360. Therefore, we have
a + b = 360, or equivalently b = 360 - a.

Since the measure of an inscribed angle is half the intercepted arc, we have
x = measure of angle QSR = (1/2)(measure of arc QR) = a/2.

Since the measure of an angle with vertex outside the circle is half the difference of the two intercepted arcs, we have

y = measure of angle QPR
= (1/2)(measure of arc QR - measure of arc QSR)
= (1/2)(a - b)
= (1/2)[a - (360 - a)]
= (1/2)(2a - 360)
= a - 180
= 2(a/2) - 180
= 2x - 180

Lord bless you!