Thread: supplementary angles.

Hello.



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

Thanks.

Hello, norifurippu!

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

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.