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@lukyanenkomax, a tool that measures the angle between two faces, or sets it, does not exist. The angle in the settings is the turn of the body about the X, Y and Z axes of the plate, so it is not related to the face of another object, as you found. Align faces brings a face parallel to another one, or against it, but cannot leave an angle between them.

A way that should get you an exact angle, though I have not tried it: first Align faces, so the two faces are parallel; then set the Rotation pivot on the edge where they meet and type the angle (15, 30) in the Rotation card; the part turns about that pivot. It works when that edge runs along X, Y or Z of the plate, because the card's axes…

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