Draw four perpendicular lines that cross each other. Like this: # except at right angles. Count the angles - 4 in the centre square, and 12 around the overlapping parts.
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16 angles, 8 of each measure - unless the transversal is perpendicular in which case, all 16 angles are right angles.
I believe that an octagon has 16 lines of symmetry.
16
A regular pentagon has no acute angles. It is possible to draw a pentagon (five sided polygon) where four of the internal angles are acute.
Including those at the boundaries of the flag, there are 16.