In rhombus ABCD, the bisector of angle ABD passes through the midpoint of side AD Find all corners of the rhombus.

Since the bisector of the angle ABD divides the side AD in half, it is also the median of the triangle ABD, and then the triangle ABD is isosceles, AB = BD. Since the lengths of all sides of a rhombus are equal, AB = AD, then BD = AD, and then the triangle ABD is equilateral.

In an equilateral triangle, all internal angles are 60, then the angle BAD of the rhombus is 60.

The sum of the adjacent angles of the rhombus is 180, then the angle ADC = 180 – 60 = 120.

The opposite angles of the rhombus are equal, then the angle ABC = 120, the angle BCD = 60.

Answer: The angles of the rhombus are 60, 120, 60, 120.

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