# The diagonal BD of parallelogram ABCD makes angles of 65 ° and 50 ° with its sides.

September 21, 2021 | education

| **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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