Draw the right triangle that has mg as the hypotenuse and the projection of mg to the inclined plane as one of its legs. This projection (i.e., its absolute value) equals F. To find one of the acute angles in this triangle use the fact that two angles are equal if their sides are perpendicular. That is, if one angle consists of rays p and q, another angle consists of rays p' and q', p is perpendicular to p' and q is perpendicular to q', then the angle measures are equal.