Geometry

In the diagram, $C$`C` is a point on $AD$`A``D` such that $AB\parallel CE$`A``B`∥`C``E` and $z=\angle BCD$`z`=∠`B``C``D`. $x$`x` and $y$`y` are two angles in $\triangle ABC$△`A``B``C`, as labelled. Prove that the sum of the two interior angles of the triangle equals the exterior angle. That is, prove that $x+y=z$`x`+`y`=`z`.

Easy

Approx 4 minutes

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