Given: ABCD parallelogram; angle BCA = 20 degrees, angle BAC = 30 degrees Find the angles of parallelogram ABCD.

In a parallelogram, opposite sides are parallel.

Then the angle BCA = CAD = 20 as criss-crossing angles at the intersection of parallel straight lines AD and BC secant AC.

Then the angle BAD = BAC + CAD = 30 + 20 = 50.

In a parallelogram, the sum of adjacent angles is 180, then the angle ABC = (180 – 50) = 130.

A parallelogram has equal opposite angles.

Angle ADC = ABC = 130, angle BCD = ABC = 50.

Answer: The angles of the parallelogram are 50 and 130.




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