The smaller diagonal AC of diamond ABCD is equal to its side. Determine the angles of the diamond.

A rhombus is a parallelogram in which all sides are equal.

The diagonal of the rhombus divides it into two equal triangles.

Consider one of them ΔABС. Since the sides of the rhombus are equal to the length of the AC diagonal, this triangle is equilateral. In an equilateral triangle, all angles are equal, and since the sum of all angles of a triangle is 180º, then:

∠BAC = ∠ABС = ∠BCA = 180º / 3 = 60º.

Since in a rhombus the sum of all angles is 360º, and opposite angles are equal, then:

∠В = ∠D;

∠А = ∠С = (360º – ∠В – ∠D) / 2;

∠А = ∠С = (360º – 60º – 60º) / 2 = 240º / 2 = 120º.

Answer: angles ∠В and ∠D are equal to 60º, angles ∠А and С are equal to 120º.