Question

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

Answer 1

In quadrilateral DPBQ:

∠1 + ∠2 + ∠B + ∠3 = 360°   ...[Angle sum property of quadrilateral]

60° + 90° + ∠B + 90° = 360°

∠B + 240° = 360°

∠B = 360° – 240°

∠B = 120°

Since, ∠ADC = ∠B = 120°  ...[Opposite angles of a parallelogram are equal]

∠A + ∠B = 180°  ...[Sum of consecutive interior angle is 180°]

∠A + 120° = 180°

∠A = 180° – 120°

∠A = 60°

So, ∠C = ∠A = 60°   ...[Opposite angle of a parallelogram are equal]