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Math Help - supplementary angles.

  1. #1
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    supplementary angles.

    Hello.



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

    Thanks.
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  2. #2
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    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.

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  3. #3
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    Thank you very much Soroban!
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  4. #4
    Member Jonboy's Avatar
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    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.
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