A rhombus is a parallelogram in which all sides are equal and the angles are not right.
Since the diagonals of the rhombus are the bisectors of its catch, then:
∠BAC = ∠САD = 28º;
∠BAD = ∠BAC + ∠CAD;
∠ВСА = ∠АСD;
∠BCD = ∠BCA + ∠ACD.
In order to find the value of the obtuse angle ∠ABС, let us first calculate the value of the acute angle ∠BAD.
∠BAD = ∠BCD = 28º + 28º = 56º.
Since the sum of all the angles of the rhombus is 360º, then:
∠ABС = ∠ADС = (360º – ∠ВАD – ∠ВСD) / 2;
∠ABС = ∠ADС = (360º – 56º – 56º) / 2 = 248º / 2 = 124º.
Answer: the magnitude of the obtuse angle ∠ABS is equal to 124º.
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