Circle Geometry Proof - Opposite Angles of a Cyclic Quadrilateral are Supplementary

Hi

I was wondering if anyone could please show me how to prove the theorem: opposite angles of a cyclic quadrilateral are supplementary. I know the way using:

Let be x.

= 2x (the angle at the centre of a circle is twice the angle at the circumference standing on the same arc DB)

360 = 2x + reflex (angle sum of point O equals 360)

reflex = 360-2x

= 180-x (the angle at the centre of a circle is twice the angle at the circumference standing on the same arc DB)

+ = x + 180 - x

+ = 180

However, I have not gotten up to the stage of proving (the angle at the centre of a circle is twice...). Could someone please show me an alternative way?

Thanx a lot!