The diagonal BD of parallelogram ABCD makes angles of 65 ° and 50 ° with its sides. Find the smaller angle of the parallelogram.
Angles B and D are equal to the sum of the angles by which the diagonal BD divides them.
B = D = 65 + 50 = 115 degrees, i.e. they are large parallelogram angles.
Since the sum of the adjacent angles of a parallelogram is 180 degrees, then
A = C = 180 – B = 180 – 115 = 65 degrees.
Answer: 65 degrees.
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