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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.
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Solution
\[\text{ Draw a parallelogram ABCD } . \]
\[\text{ Drop a perpendicular from B to the side AD, at the point E } . \]
\[\text{ Drop perpendicular from B to the side CD, at the point F } . \]
\[\text{ In the quadrilateral BEDF }: \]
\[\angle EBF = 60°, \angle BED = 90°\]
\[\angle BFD = 90°e \]
\[\angle EDF = 360° - (60° + 90° + 90°) = 120°\]
\[\text{ In a parallelogram, opposite angles are congruent and adjacent angles are supplementary } . \]
\[\text{ In the parallelogram ABCD }: \]
\[\angle B = \angle D = 120° \]
\[\angle A = \angle C = 180°e - 120° = 60 °\]
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