I encountered this problem in Physics and the direction chosen by me was different from that used in the answer hence I got the wrong answer. The problem here is in the mathematical interpretation of a statement hence I'm posting it on Maths SE. The question goes like this:
A ray of light makes an angle of $10^\circ$ with the horizontal above it and strikes a plane mirror which is inclined at some angle to the horizontal. We need to find the angle for which the light becomes vertical after reflection.
However I think this diagram is wrong; and when it states that it makes the angle "with the horizontal above it", it should indicate that the light ray would make an angle of $10^\circ$ clockwise with the horizontal. If I use that, I get the answer to be $40^\circ$.
In the picture bellow is the third angle in the triangle denoted $\beta.$ Then $$10^{\circ}+180^{\circ}-\theta + \beta=180^{\circ},$$ therefore $$\beta=\theta-10^{\circ}.$$