Kiselev's Geometry Problem 51

Question

I am going through Kiselev's Geometry, Book I. I am having trouble with problem 51. The problem states:

Give an example that disproves the proposition: "If the bisectors of two angles with a common vertex are perpendicular, then the angles are supplementary." Is the converse proposition true?

His definition of a supplementary angle goes as follows:

Two angles [...] are called supplementary if they have one common side, and their remaining two sides form continuations of each other. [...] the sum of two supplementary angles is 180°.

But I cannot see how to disprove that proposition using his definition. Is it something lost in translation or is it something that I am missing?

Answer 1

Does this picture provide some help?

Answer 2

Hint: Angles can share a vertex without sharing a side.