Answer:
Examples to disprove them are as follows;
1) Angles of two different inscribed regular polygon in contact at their vertices
2) Angles on the opposite corners of a regular even sided polygon
Step-by-step explanation:
The statement to be disproved can be presented as follows;
1) ∠A and ∠B share a common vertex
2) The bisectors of ∠A and ∠B create one line then
∠A and ∠B are vertical, that is ∠A and ∠B are on the opposite sides of the point where two lines cross or ∠A = ∠B
Given that ∠A = Interior angle of a inscribed square = 90°
∠B = Interior angle of an inscribed equilateral triangle = 60°
Therefore the two circles can be arranged such that the line connecting the centers of both circles, are the bisectors of ∠A and ∠B
However, ∠A ≠ ∠B hence the two angles are not vertical QED
(2) The angles ∠A and ∠B where ∠A = ∠B are on the opposite corners of an even sided regular polygon are equal and their bisectors belong to the same line, however, it can be shown that ∠A and ∠B are not vertical.
