A diagonal and a side of a rhombus are of equal length. Find the measure of the angles of the rhombus.

Dear Student

Let ABCD be the rhombus.
Thus, AB = BC = CD = DA

Given that a side and diagonal are equal.
AB = BD (say)
Therefore, AB = BC = CD = DA = BD
Now, all the sides of a triangle ABD are equal.
Therefore, ΔABD is an equilateral triangle.
Similarly,
ΔBCD is also an equilateral triangle.
Thus, ∠A = ∠ABD = ∠ADB = ∠DBC = ∠C = ∠CDB = 60°
∠B = ∠ABD + ∠DBC = 60° + 60° = 120°
And
∠D = ∠ADB + ∠CDB = 60° + 60° = 120°
Hence, the angles of the rhombus are 60°, 120°, 60° and 120°.

Thanks