The heights of the parallelogram drawn from one vertex form angles of 40 and 60 degrees

The heights of the parallelogram drawn from one vertex form angles of 40 and 60 degrees at the intersection with the diagonal. Find the angles of the parallelogram.

Consider a triangle BOO1, for which, by condition, the angle BOO1 = 60, BO1O = 40, then the angle OBO1 = 180 – 60 – 40 = 80.

Consider a quadrangle ВKDН, in which the angle KВН = 80, and the angles ВНD and ВКD are straight, then the angle НDK = 360 – 80 – 90 – 90 = 100.

A parallelogram has opposite angles, and the sum of adjacent angles is 180.

Then: angle ABC = ADС = KDН = 1000, angle ВAD = ВСD = 180 – 100 = 80.

Answer: The angles of the parallelogram are 80 and 100.