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A diagonal and a side of a rhombus are of equal length. Find the measure of the angles of the rhombus. A diagonal and a side of a rhombus are of equal length. Find the measure of the angles of the rhombus.
Dear StudentLet ABCD be the rhombus.Thus, AB = BC = CD = DAGiven that a side and diagonal are equal.AB = BD (say)Therefore, AB = BC = CD = DA = BDNow, 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
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