A, B, C, D are four points, and AB, BC subtend (i.e. are opposite to) supplementary angles at D: show that A, D, C are in the same straight line.

Question

$A, B, C, D$ are four points, and $AB, BC$ subtend (i.e. are opposite to) supplementary angles at $D$: show that $A, D, C$ are in the same straight line.

(Question from Barnard and Child's Elements of Geometry, 1914. )

I'm unable to visualise the problem. Can someone help me out. Thanks.

Answer 1

I think there is very little to explain: it is the very definition of supplementary.

Below there is a picture