Do it logically, or otherwise

Image from https://app.geogebra.org/#geometry.

Let the cube have side length x. (I assume it is a cube)

The image above is a cross-section of the plane containing the diagonals.

It is a rectangle with sides $x$ and $\sqrt{2}x$ .

By Pythagorean Theorem, the half-diagonal has length $\frac {\sqrt{3}}{2}x$ .

By cosine rule, $(\sqrt {2}x)^2 = 2(\frac {\sqrt {3}}{2}x)^2(1-\cos @)$ $2x^2 = \frac {3}{2}x^2(1-\cos@)$ $\frac {4}{3} = 1-\cos@$ $@ = \arccos (-\frac {1}{3})$

This is approximately equal to $109$ degrees and $28$ minutes. The final answer is $A+B = 109+28 = \boxed {137}$

Joining each alternate vertex forms a tetrahedron.and it's center is the center of cube. as you all know angle between line joining center and vertex is 109 degree 28 minute, answer is 137