Answer:
see below
Step-by-step explanation:
Hi there!
We're given the triangle ABC with lines AC and BC extended to get the lines AD and BE.
<DEC is formed by lines AD and BE, with C as the vertex.
We're also given that <4≅<5.
You may notice that <DCE and <5 are vertical angles, which means that they share the same vertex (vertex C), and are opposite to each other.
There is a theorem that states vertical angles are congruent.
therefore, <DCE≅<5 by vertical angle's theorem.
But we need to prove that <DCE≅<4
There is a property known as transitivity, where if a=b and b=c, then a=c.
Since both <DCE and <4 are congruent to <5, they also must be congruent to each other via transitivity
Hope this helps! :)
