Measure of angles is the same

Question

I found the following theorem in a lecture notes without proof: Let $A, B, C, D, E$ and $F$ be points on the plane such that $\angle ABC$ and $\angle DEF$ are either both acute or they are both obtuse. If $AB$ is perpendicular to $DE$ and $BC$ is perpendicular to $EF$ then $\angle ABC=\angle DEF$. I was able to see the acute angle case but why do those both angles can both be obtuse? And how to prove the obtuse case?

Answer 1

IF you know spanish, this page will be usefull:

https://es.wikipedia.org/wiki/Arco_capaz

After you draw a sketch for the obtuse angle case, consider the complementary angles and those are equal because they share an arc of a circumference. Then the complementary angles are equal.