Each side of the dodecagon subtends an angle of 30^° at the centre of the circumcircle of the figure (the circle which passes through all 12 of its vertices).

Angle AOP = 90^° so OPA = 45^°

Angle BOP = 120^° so OPB = 30^°

Therefore APB = 45^° + 30^° = 75^°

Alternatively, ÐAOB = 150^° and, as the angle subtended by an arc at the centre of a circle is twice the angle subtended by that arc at a point on the circumference, ÐAPB = 75^°.