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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.
Solution
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]
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