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Question 3
The angel between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 60. Find the angles of the parallelogram.

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Solution

Let the a parallelogram be ABCD in which ADC and ABC are obtuse angles. Now, DE and DF are two altitudes of parallelogram and angle between them is 60

Now BEDF is a quadrilateral, in which BED=BFD=90
FBE=360(FDE+BED+BFD)
=360(60+90+90)
=360240=120
Since, ABCD is a parallelogram.
ADC=120
Now, A+B=180 [sum of two cointerior angles is 180]
A=180B
=180120[FBE=B]
A=60
Also, C=A=60
Hence, angles of the parallelogram are 60,120,60 and 120, respectively.


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