a circle proof

[Phebotalus]

Hi there! I'm in grade 12 and I'm having a bit of trouble with this question:

AB and CD are two chords of a circle with centre O, which intersect at right angles at E.
Prove angle BOC + angle AOD = 180 degrees.

Thank you very much!

 

[pka]

\(\displaystyle \L
\angle AEB = \frac{1}{2}\left( {arc(CB) + arc(AD)} \right)\)

Now \(\displaystyle \L
\angle AOB\) is the central angle of \(\displaystyle \L
arc(CB)\) and \(\displaystyle \L
\angle AOD\) is the central angle of \(\displaystyle \L
arc(AD)\) .
You put that together to complete your proof.

 

[Phebotalus]

I'm not sure I quite understand how that prooves it. Specifically, how do you know angle AEB=1/2(arc(CB) + arc(AD))? As far as I know of, I have not learnt any property of circles arcs helping with angles...
Do you think you could explain the solution further?