In a rhombus, one of the diagonals is equal to the side. find the corners of the diamond.

Given:
rhombus ABCE,
AC diagonal,
AC = AB = BC.
Find the degree measures of the rhombus angles: angle A, angle B, angle C, angle E -?
Decision:
1. Consider the triangle ABC. He is equilateral. Therefore, angle B = angle BAC = angle BCA = 60 degrees.
2. Consider a rhombus ABCE. Its opposite angles are equal to each other, then angle A = angle C, angle B = angle E = 60 degrees. Knowing that the sum of the degree measures of the parallelogram is 360 degrees, we get:
angle A = angle C = (360 – 60 – 60): 2 = 120 degrees.
Answer: 120 degrees; 120 degrees; 60 degrees; 60 degrees.