How to find arc angle with known other arc?

Question

Take a look at the draft, please. I need to build arc1 from one point to another with given radius. For this i need to know start and end angles a4 and a5. This is the requirements of programming library i use.

I suppose i can find a5 easely as a4 + 2*a1. So the question is how to find a4.

Ark width w, length of perpendicular p to the w, angles a1 and a2, and radius r are known. Angle a3 is 90 degrees.

Coordinate system of this circle starts from right and goes clockwise. In this particular case on the draft start of the arc will be 195°, end 95°.

Answer 1

First, $a_5 = 360^\circ - (a_4 + 2a_1)$

Now, beyond that, I was about to say there simply is not enough information to determine a specific $a_4$ or $a_5$. Put another way, that triangular wedge can slide all around that circle and be located anywhere.

But then I read you last sentence "In this particular case on the draft start of the arc will be 195°, end 95°." I find this way of phrasing it to be confusing, but it sounds like either $a_4$ or $a_5$ must be $95^\circ$, and it looks like $a_4 \approx 95^\circ$ in the draft.

Answer 2

My question in origin has no solutions, this is why i accept @bob.sacamento answer. But in practice, as soon i build all shapes by self, i can calculate a4 as angle of SSS triangle. Two sides of this triangle are radius length, and third (opposite to a4 can be calculated. From there a4 = arcos(b^2 + c^2 - a^2 / 2bc).

Click to see draft