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The formula for each interior angle of a regular polygon of n sides is:  (n - 2)(180^o)/n

 

For a regular hexagon:  (6 - 2)(180^o)/6  =  120^o.

For a regular pentagon:  (5 - 2)(180^o)/5  =  108^o.

 

For the red triangle that is outside the blue hexagon, the two base angles are each: 

    (180^o - 108^o) / 2  =  36^o.

This means that each base angle of the dark-red trapezoid is 108^o - 36^o  =  72^o.

 

Subtracting this from the hexagon angle, we get  120^o - 72^o  =  48^o