The angle between the two altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is 30°. The measure of the obtuse angle is

BE & EF are perpendiculars from the same point

∠ EBF = 30⁰(given)

Sum of interior angles of a quadrilateral = 360⁰

∠ EBF + ∠ BED + ∠ EDF + ∠ DFB = 360⁰

∠ EDF = 360⁰-(90⁰ + 90⁰ + 30⁰)

∠ EDF = 150⁰ which is an obtuse angle.