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

Question

Philoid · Accepted Answer

Given ABCD is parallelogram in which DP is perpendicular to AB and DQ is perpendicular to BC.

Given,

In quad. DPBQ, by angle sum property we have,

So (opposite angles in parallelogram are equal)

Since, AB||CD (opposite sides are parallel in parallelogram),

(Sum of adjacent interior angles is )

So