The bisector of the angle of a parallelogram, as a result of intersection with its side, creates angles, the degree measure

The bisector of the angle of a parallelogram, as a result of intersection with its side, creates angles, the degree measure of which is 1: 3. Determine the type of parallelogram.

Let us determine the values of the angles AKВ and AKС, formed by the bisector AK and the side BC.

Let the angle AKB = X0, then the angle AKС = 3 * X0.

The sum of the angles AKВ + AKC = 180.

X + 3 * X = 180.

X = 180/4 = 45.

Angle AKВ = 45, angle AKС = 45 * 3 = 135.

By the property of the bisector, the AВK triangle is isosceles, then the angle ВAK = 45.

The angle DАК = ВAK = 45, since AK is the bisector of the angle ВAD, then the angle ВAD = VAK + DАК = 45 + 45 = 90, and therefore, AВСD is a rectangle.

Answer: Parallelogram AВСD rectangle.