Diagonal AC is drawn in rhombus ABCD. Find the obtuse angle ABC if the CAD angle is 28 °.

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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