# supplementary angles.

• May 31st 2008, 01:39 PM
norifurippu
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.
• May 31st 2008, 01:54 PM
Soroban
Hello, norifurippu!

Quote:

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 $\angle ABC$ ?

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

• May 31st 2008, 02:08 PM
norifurippu
Thank you very much Soroban!
• May 31st 2008, 02:37 PM
Jonboy
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.