According to the Journal of Irreproducible Results, any obtuse angle is a right angle! Here is
their argument.
Given the obtuse angle x, we make a quadrilateral ABCD with  DAB = x, and  ABC =
90◦, andAD = BC. Say the perpendicular bisector toDC meets the perpendicular bisector to
AB at P. ThenPA = PB andPC = PD. So the trianglesPADandPBC have equal sides
and are congruent. Thus  PAD =  PBC. But PAB is isosceles, hence  PAB =  PBA.
Subtracting, gives x =  PAD−  PAB =  PBC −  PBA = 90◦. This is a preposterous
conclusion – just where is the mistake in the “proof” and why does the

Question

According to the Journal of Irreproducible Results, any obtuse angle is a right angle! Here is
their argument.
Given the obtuse angle x, we make a quadrilateral ABCD with  DAB = x, and  ABC =
90◦, andAD = BC. Say the perpendicular bisector toDC meets the perpendicular bisector to
AB at P. ThenPA = PB andPC = PD. So the trianglesPADandPBC have equal sides
and are congruent. Thus  PAD =  PBC. But PAB is isosceles, hence  PAB =  PBA.
Subtracting, gives x =  PAD−  PAB =  PBC −  PBA = 90◦. This is a preposterous
conclusion – just where is the mistake in the “proof” and why does the

anonymous · Answer

0-0=0
you can't work with zeroes like that in geometry. 
it's the equivalent of dividing by zero in algebra.