The values of the two angles of the parallelogram are proportional to 4 and 5.

The values of the two angles of the parallelogram are proportional to 4 and 5. Find the angle between the heights of the parallelogram drawn from the apex of the obtuse angle.

The sum of the adjacent angles of a parallelogram is 180.

Let the angle ABC = 5 * X0, then, by condition, the angle BCD = 4 * X0.

5 * X + 4 * X = 180.

9 * X = 180.

X = 180/9 = 20.

Then the angle ABC = 20 * 5 = 100.

In a parallelogram, the opposite angles are equal, then the angle ADC = ABC = 100. Consider a quadrilateral NВKD in which the angle NDK = 100, and the angle BHD = BKD = 90.

Then the angle НВК = 360 – 100 – 90 – 90 = 80.

Answer: The angle between the heights is 80.