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Compound Miters
I’m trying to a make a minature groin vault (right angle intersection of two semicircular arches. I’ve made matched keystone-shaped slats to line the arch: they run perpendicular to the face of the arch with the bottom of each keystone running flush and tangent to the arc of the arch.

The arch radius is 7 inches and uses 13 “keystone-shaped” slats .844 inches wide at the base with sides at 7 degrees form the base. I placed a keystone at the top of the arch then lay the others around in succession to fill it in. Resulting angles from the top keystone to each succeeding keystone face were 14, 28, 42, 56, 70 and 84 degrees.

The miter calculation was straighforward: So miters were

Slat Miter Miter
Face Ang Ang
Ang Calc Used
14 44.3 44.5
28 41.6 41.5
42 36.8 37
56 29.3 29.5
70 19 19
84 6 6

Miter anlgle calc = arctan ((cos (slatface angle)*.844)/.844)

But how do I calculate the compound angle?