# Math Help - supplementary angles.

1. ## supplementary angles.

Hello.

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

Thanks.

2. Hello, norifurippu!

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.

3. Thank you very much Soroban!

4. 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.