Two sides of a parallelogram measure 15cm and 20 cm, and one of the diagonals measures 19cm. What are the measures of the angles of a parallelogram to the nearest degree."?
63.9 deg, 116.1 deg
As one of the sides is 20 cm (> 19 cm), the 19 cm diagonal is the smaller of 2 diagonals.
Let's draw a line AB of length 20 cm. At A let's draw a circle with a radius of 15 cm and at B let's draw another circle with a radius of 19 cm. Let's say they meet at point C. From C let's draw a line CD of 20 cm length parallel to line AB. Note that, point D lies at the side same as B. Let's join point D with point B. We have our parallelogram ABDC. Let's measure the angles CAB and ABD.