supplementary angles.

Hello.
http://img233.imageshack.us/img233/7257/circlepd7.jpg
http://img71.imageshack.us/img71/8823/solutionep0.jpg

Here I understand why angle 'AED' is a supplement for angle 'DEC', but why is 'ABC'?

Thanks.

Hello, norifurippu!

Quote:

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http://img233.imageshack.us/img233/7257/circlepd7.jpg
http://img71.imageshack.us/img71/8823/solutionep0.jpg

Here I understand why is a supplement for , but why is ?

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is a cyclic quadrilateral (inscribed in a circle).
. . Hence, its opposite angles are supplementary.

Thank you very much Soroban!

you could just reason it as m<AED is a supplement to m<DEC, m<ABC = m<AED, thus they have the same measure, so m<ABC is also a supplement of m<DEC.