The angle between the two altitudes of a parallelogram through the vertex of an obtuse angle is 50∘50 ∘ . Find the angles of parallelogram.

The problem states that the angle between the two altitudes of a parallelogram through the vertex of an obtuse angle is 50 degrees.

In a parallelogram, the altitudes drawn from the vertices of an obtuse angle are perpendicular to the opposite sides. Therefore, these altitudes form a right angle with the sides of the parallelogram.

Since the altitudes form a right angle with the sides, the angle between the altitudes is the supplement of the obtuse angle of the parallelogram.

The problem states that this angle is 50 degrees. Therefore, the obtuse angle of the parallelogram is 180 - 50 = 130 degrees.

In a parallelogram, opposite angles are equal. Therefore, the other obtuse angle is also 130 degrees.

The sum of the angles in a parallelogram is 360 degrees. Therefore, the acute angles of the parallelogram are each (360 - 130 - 130) / 2 = 50 degrees.

So, the angles of the parallelogram are 130 degrees and 50 degrees.