Counter-example to this property in euclidean geometry?

Question

I have to prove that this property is false, finding a counter-example.

If $\widehat{A}=\widehat{C}=90^{\circ}$ then the convex quadrilateral $ABCD$ is a rectangle.

I can't find any counter-example with this measure of angle because this property seems to be true. I took a right trapezoid $ABCD$ but it's $\widehat{A}=\widehat{D}=90^{\circ}$...

I'm probably blind...

Thanks in advance !

Answer 1

Take two right angles as follows, rotate one to some small angle then make them intersect.

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Answer 2

Let's assume four points on a circle such that a pair of them are endpoints of a diameter and other vertices are on different part of semi circles.

These four points can determine infinitely many quadrilaterals which are not rectangles