How to work out angles for cutting a handrail corner?

[matsw]

Anyone know how to calculate the compound angles for cutting a pigs ear handrail for an inside corner?

The rail on both walls is to be fitted at an angle of 20 degrees from the horizontal. The corner is 90 degrees.

I thought it would be simply a cut of 45 degrees and 20 degrees on both ends but I was wrong as the outer part of the rail does not match up, even though they but up correctly.

 

[imroberts]

Are you sure the stairs are at an angle of 20 degrees?

That sounds very shallow for stairs, I'm sure mine are around 40 degrees.

 

[matsw]

The banisters are to be at 20 degrees due to the corner steps. They change to 40 degrees when they then follow the normal treads.