One of the corners of the rhombus is 64 degrees. Find the corners that the side of the diamond forms with its diagonals.

Given: ABCD – rhombus, AC and BD – diagonals, angle A is equal to 64º.

Find: angle CAB, angle ABD.

Solution:

Angle CAB – the angle formed by the side AB and the diagonal AC, which lies on the bisector AC of the angle DAB, equal to 64º. The CAB angle is 32º.
Angle ABD – the angle formed by the side AB and the diagonal BD, which lies on the bisector BD of the angle ABC, equal to 180º – 64º = 116º (The sum of the angles adjacent to one side of the rhombus is 180º). The ABD angle is 58º.
The opposite angles of the rhombus are equal, therefore, the angles that each side of the rhombus forms with its diagonals will be 32º and 58º.
Answer: 32º and 58º.