Find the corners of the rhombus where the height bisects the side.

Given:
rhombus ABCE,
ВН height,
CH = НЕ.
Find the degree measures of the angles of the rhombus ABCE, that is, angle A, angle B, angle C, angle E -?
Decision:
1. Consider the CBE triangle. Since BH is the height and median, the CBE triangle is isosceles. Therefore, the angle C = angle НEB.
2. Consider a rhombus ABCE. Its opposite angles are equal to each other, then the angle A = angle C, angle B = angle E. The diagonals of the rhombus are the bisectors of the angles. Let the angle C = angle A = x degrees, then angle B = angle E = 2 * x degrees. We know that the sum of the degree measures of a parallelogram is 360 degrees. Let’s make the equation:
x + x + 2 * x + 2 * x = 360;
6 * x = 360;
x = 360: 6;
x = 60 degrees – the degree measure of the angles A and C;
2 * 60 = 120 degrees – the degree measure of the angles B and E.
Answer: 60 degrees; 60 degrees; 120 degrees; 120 degrees.