Question

The angle between the altitudes of a parallelogram, through the same vertex of an obtuse angle of the parallelogram is 60°. Find the angles of the parallelogram.

 

Answer 1

\[\text{ Draw a parallelogram ABCD } . \]

\[\text{ Drop a perpendicular from B to the side AD, at the point E } . \]

\[\text{ Drop perpendicular from B to the side CD, at the point F } . \]

\[\text{ In the quadrilateral BEDF }: \]

\[\angle EBF = 60°, \angle BED = 90°\]

\[\angle BFD = 90°e \]

\[\angle EDF = 360° - (60° + 90° + 90°) = 120°\]

\[\text{ In a parallelogram, opposite angles are congruent and adjacent angles are supplementary } . \]

\[\text{ In the parallelogram ABCD }: \]

\[\angle B = \angle D = 120° \]

\[\angle A = \angle C = 180°e - 120° = 60 °\]