If line segment ac is perpendicular to line segment cb and the measurement of angle cbd is 125 degrees then the measurement of angle a equals?

Here is the problem with this question. If AC is perpendicular to CB, then they must share a common endpoint, namely C. And we know that angle ACB must be a right angle. Now in order to make CBD 125 degrees, we need to draw it so it is greater than a right angle. So draw the line AC and at the point C, drop a perpendicular downwards and this is CB. Now D must be to the left and below B in order for the angle to be 125.

Here is the catch.. We were never given any info about angle A, we only have point A. So one assumption would be to connect D and A and make segment AD. Then we have a quadralateral with two angle know, namely 125 and which is CBD and 90 which is ACB. The sum of the angles is 360 so the other two must be 360-(125+90)=145. This would be the sum of angles CAD and BDA.

The length of segment BD would determine angle CAD and we do not know that

So we don't have enough information.

then the measurement of angle A equals: