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 $\displaystyle \angle DAB$ be x.

$\displaystyle \angle DOB$ = 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$\displaystyle \angle DOB$(angle sum of point O equals 360)

reflex$\displaystyle \angle DOB$= 360-2x

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

$\displaystyle \angle DAB$ + $\displaystyle \angle DCB$ = x + 180 - x

$\displaystyle \angle DAB$ + $\displaystyle \angle DCB$ = 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!