# The diagonal AC of parallelogram ABCD makes an angle of 20⁰ with side AB.

The diagonal AC of parallelogram ABCD makes an angle of 20⁰ with side AB. Find the corners and sides of a parallelogram if its perimeter is 16 cm.

The sum of the adjacent angles of the parallelogram is 180, then the angle BAD = 180 – 140 = 40.

Since the angle ABC = 20, then the angle CD = 40 – 20 = 20, then AC is the bisector of angle A.

Angle ACB = CAD as criss-crossing angles at the intersection of parallel lines AD and BC secant AC. Then the angle BAC = BCA, and accordingly, the triangle ABC is isosceles.

Since the opposite sides of the parallelogram are equal, then AB = BC = CD = AD.

Then the side of the parallelepiped is: AB = 16/4 = 4 cm.

The opposite angles of the parallelogram are equal, BAD = BAD = 40, ABC = ADC = 140.

Answer: The angles are 40 and 140, the sides are 4 cm.

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