Q. 215.0( 3 Votes )

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

Answer :



Given ABCD is a parallelogram in which DPAB and AQ BC.
Given
PDQ = 60°
In quad. DPBQ
PDQ + DPB + B + BQD = 360° [Sum of all the angles of a Quad is 360°]
60° + 90° +
B + 90° = 360°
B = 360° – 240°
Therefore,
B = 120°
But
B = D = 120° [Opposite angles of parallelogram are equal]
B + C = 180° [Sum of adjacent interior angles in a parallelogram is 180°]
120° +
C = 180°
C = 180° – 120° = 60°
Therefore,
A = C = 70° (Opposite angles of parallelogram are equal)


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