ABCD is a parallelogram. BCA = 15 and ADC = 130 degrees. Calculate the degree measures of the angles ABC and ACD.

Let’s find the angle ABC.
ABCD is a parallelogram, and the opposite angles of the parallelogram are equal, therefore, the angle ABC is equal to the angle ADC and is equal to 130 degrees.
Find the ACD angle.
Knowing that the sum of the angles of the quadrilateral is 360 degrees, we will compose the equation:
ABC + ADC + BCA + CAD + ACD + CAB = 360;
130 + 130 + 15 + 15 + ACD + CAB = 360;
ACD = CAB = X (criss-crossing angles are equal);
2 x X = 360 – (130 + 130 + 15 + 15);
2 x X = 70;
X = 70/2;
X = 35 degrees.
Answer: ADC angle = 130 degrees, ACD angle = 35 degrees.