Is the proposition "all equal angles are opposite vertex angles" true? If not, please give counter examples

Is the proposition "all equal angles are opposite vertex angles" true? If not, please give counter examples

no
If one angle is on one sheet of paper and the other is on another sheet of paper, and the angles are equal, then the two angles are not opposite to the vertex

The converse theorem of the reciprocal sum of two acute angles of right triangle

Mutual complement of two acute angles of right triangle
The inverse theorem is that a triangle is a right triangle if there are two angles complementary to each other
Established
There is no inverse theorem for vertex angle equality

Why is "the middle line on the hypotenuse of a right triangle equal to half of the hypotenuse"?
Learning at a loss, why on earth?

Very simple, let ABC be the triangle, C be the right angle, and d be the midpoint of ab
Through D, De is perpendicular to AC, and through D, DF is perpendicular to BC
It is easy to prove that triangle ade is equal to triangle DBF, so de = BF
It is also easy to prove that de = CF, so CF = BF
Then prove that triangle DCF and triangle DBF are congruent
Let AB be the inverse of a triangle, and let CD = AB be the center line
From ad = CD, angle DAC = angle DCA
From BD = CD, angle DBC = angle DCB
And because angle ACB = angle DCA + angle DCB
So angle DAC + angle DCA + angle DBC + angle DCB = 180 degrees
From the angle DAC = angle DCA, angle DBC = angle DCB, angle DCA + angle DCB = 90 degrees
So ABC is a right triangle