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.

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- May 31st 2008, 12:39 PMnorifurippusupplementary 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. - May 31st 2008, 12:54 PMSoroban
Hello, norifurippu!

Quote:

http://img233.imageshack.us/img233/7257/circlepd7.jpg

http://img71.imageshack.us/img71/8823/solutionep0.jpg

Here I understand why $\displaystyle \angle AED$ is a supplement for $\displaystyle \angle DEC$, but why is $\displaystyle \angle ABC$ ?

$\displaystyle BCED$ is a cyclic quadrilateral (inscribed in a circle).

. . Hence, its opposite angles are supplementary.

- May 31st 2008, 01:08 PMnorifurippu
Thank you very much Soroban!

- May 31st 2008, 01:37 PMJonboy
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.