The angle between the heights of the parallelogram drawn from the apex of this angle

The angle between the heights of the parallelogram drawn from the apex of this angle is 4 times this angle. Find the angles of this parallelogram.

Draw two heights from the top of the acute angle, AH and AK.

Let us denote the sought angle by X0. Angle BAD = X0, then, by condition, angle HAK = 4 * X.

In the resulting quadrangle AHCK, the angle HAK = 4 * X, the angle AHC and AKC = 90, as heights, the angle HCK = X, as opposed to the angle BAD. The sum of these angles is 360.

360 = 4 * X + 90 + X + 90.

5 * X = 180.

X = 180/5 = 36.

Angle BAD = BCD = 36.

Since the sum of the adjacent angles of the parallelogram is 180, the angle ABC = ADC = 180 – 36 = 144.

Answer: The angles of the parallelogram are 36 and 144 degrees.