Question

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

Answer 1

∠A = ∠C = 60°

∠B = ∠D = 120°

Explanation:

In quad. DPBQ, by angle sum property we have

∠PDQ + ∠DPB + ∠B + ∠BQD = 360°

60° + 90° + ∠B + 90° = 360°

∠B = 360° – 240°

Therefore, ∠B = 120°

But ∠B = ∠D = 120° opposite angles of parallelogram

As, AB || CD opposite sides of a parallelogram

∠B + ∠C = 180° sum of adjacent interior angles is 180°

120° + ∠C = 180°

∠C = 180° – 120° = 60°

Hence ∠A = ∠C = 60° Opposite angles of parallelogram are equal