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The angle is tan-1(M/E)*(D/R)2

where

M is the mass of the earth,

E is the mass of the mountain,

R is the distance of the plumb bob from the centre of mass of the earth - near enough the earth's radius,

D is the distance of the bob from the centre of mass of the mountain.

Both M/E and D/R will be small so that the angle will also be small. In that case, the tangent of the angle will be close to the angle itself (measured in radians). So the angle of deflection is approximately (M/E)*(D/R)2 radians.

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