The angle between the two altitudes of a parallelogram through the vertex of
an obtuse angle is 50°. Find the angles of a parallelogram.
Answers
Answer: The angle between the two altitudes of a parallelogram through the vertex of an obtuse angle is 50°.
To Find : the angles of a parallelogram.
Solution:
∠DAN = ∠BNA = 90° ( alternate angle ) as AD || BC and AN transversal
∠BAM = ∠DMA = 90° ( alternate angle ) as AB || CD and AM transversal
∠DAN = ∠MAN + ∠DAM = 90°
∠BAM = ∠BAN + ∠MAN = 90°
=> ∠MAN + ∠DAM + ∠BAN + ∠MAN = 90° + 90°
∠MAN + ∠DAM + ∠BAN = ∠DAB
=> ∠DAB + ∠MAN = 180°
=> ∠DAB + 50°= 180°
=> ∠DAB = 130°
∠A = 130°
opposite angles of parallelogram are equal
Hence ∠D = 130°
Sum of adjacent angles of parallelogram = 180°
Hence ∠B = ∠D = 50°
Another Simpler method
in Quadrilateral AMCN
50° + 90° + ∠C + 90° = 360°
=> ∠C = 130°
∠A =∠C = 130°
∠B = ∠D = 50°
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