Solution of the Week #399 - What's Wrong

That OAB and BDC are equal presupposes that AC and BD are parallel. This is an unwarranted assumption.

Instead we should work out what the angle AOB is. If OAB is indeed 32 degrees, then to complete the 180 degrees of the triangle OAB, angle AOB should be 58 degrees.

Alternatively, if we assume CDB is indeed 32 degrees, then from the central angle theorem, AOB is equal to twice 32: 64 degrees.

So both marked angle being 32 degrees leads to a contradiction.

If OAB is 32 degrees, BDC is 29 degrees, whereas if BDC is 32 degrees, OAB is 26 degrees. The only time they can be equal is if they are both equal to 30 degrees.